%% Version dated January 4, 1996 REFERENCES FOR LEAST SQUARES METHODS {\AA}ke Bj{\"o}rck This is the BibTeX reference base which I have used for the book Numerical Methods for Least Squares, SIAM, 1996 (reference {bjor:96}). It is available by anonymous ftp at math.liu.se in the directory pub/references It has been modeled after the BibTeX reference base of Pete Stewart, and the same comments applies to its use. Below I repeat some of the introductory comments of his base: CITATION KEYS A citation key is divided into two fields, :, separated by a colon. The author field is constructed as follows. If there is only one author, the first four letters of his or her last name are used to form the field (but only one letter each from prefixes, e.g. van de Geign becomes vdge). If there are two authors the first two letters in their last names are used. If there are three authors the first two letters of the first are used with one letter from each of the second and third. If their are four, one letter from each is used. Warning: there may be a few exceptions to these conventions. NAMES Names appear in the order in which they appear in the reference, and entries are alphabetized by the first name to appear. To keep BibTeX from becoming confused, only initials of given names are used. Between some entries you will find clusters of two letters--e.g. -ac- -ad-. These can be used to position yourself within the reference base. KEYWORDS Each entry has a keyword field, labeled kwds. The program bibsrch (see below) will search the file for matches in a user-specified combination of conjunctions, disjunctions, and negations. The user can also specify the author. The program getkey dumps the keywords on the standard output. To get an alphabetized list of all key words from the file ref.bib try getkey ref | sort -uf > keywords The choice of key words is a highly personal matter. I have used a number of abbreviations to keep the kwds field to a manageable size. Here they are. approximate methods (appr) augmented system (augms) backward perturbation (pert), banded least squares (band), blas (blas), block angular system (basys), block methods (block), Chebyshev approximation (cheb), Cholesky (chol), condition (cond), conjugate gradients (cg), constrained least squares (constr), control theory (contr), covariance matrix (covar), CS decomposition (csd), downdating (downd), eigenvalue problem (eigv) equilibration (scale), error estimate (err), fast Fourier transform (fft), fill-in (fill), generalized eigenvalue problems (geig), generalized inverse (ginv), generalized linear model (glsq), generalized QR decomposition (gqrd), geodesy (geod), geometric elements, fitting (geom), generalized singular value decomposition (gsvd), Givens rotation (rot), graph theory (graph), Gram-Schmidt (grsch), history of least squares (hist), Householder (house), hyperbolic rotation (hyp), ill-posed (illp), interior point methods (intpoint), interval analysis (err), iterative method (iter), iterative refinement (ir), Kronecker product (kron), Lanczos (lanczos), linear algebra general (la), LU decomposition (lud), matrix approximation (max), nested dissection (nestdis), nonlinear least squares (nlsq), normal equations (ne), numerical linear algebra (nla) optimization (opt), ordering for sparsity (perm), orthogonalization (orth), orthogonal regression (orthreg), precision (err), preconditioning (precond), pseudo-inverse (ginv), parallel computation (prll), perturbation theory (pert), polynomial approximation (poly), projection (orth), QR decomposition (qrd), quadratic programming (quadpr), random matrix (rand), rank degenerate problems (rank), rank revealing QR factorization (rrqrd), recursive least squares (rls), regularization (regul), regression (regr), robust estimation (rob), scaling (scale), signal processing (sigp), singular value decomposition (svd), software (soft), sparse (sparse), spline approximation (spline), statistics (stat), survey paper/book (survey), systolic (syst), test matrix (test), Toeplitz (toep), total least squares (tls), underdetermined systems (uds), updating, downdating (upd, downd), Vandermonde systems (vand), variable projection (varpro), vector processing (prll), weighted least squares (wlsq)" The program getkey also prints out these correspondences in the appropriate places. (They are actually key words in the last article of the base; take a look.) DISCLAIMERS Do not use the references in a paper, unless you have checked them out for yourself. Naturally, I am interested in hearing about any errors you may find. This reference base downdated regularly, and items can disappear. For example, I will generally remove techreports as I find them published in journals. If you use this base in a \bibliograpy command, save your bbl files! BIBSRCH The programs bibsrch and getkey, written by G.W. Stewart, may be generated from the file bibsearch.tar, available by anonymous ftp at thales.cs.umd.edu in the directory pub/references. Simply place bibsearch.tar in the directory where you want the directory containing the programs. Then tar xf bibsearch.tar cd bibsearch more README and you will be told what to do next. @article{abde:71, author = "N. N. Abdelmalek", year = "1971", title = "Roundoff Error Analysis for {Gram-Schmidt} Method and Solution of Linear Least Squares Problems", journal = "BIT", volume = "11", pages = "345--368", kwds = "err,grsch,qrd" } @article{adco:1878, author = "R. J. Adcock", year = "1878", title = "A Problem in Least Squares", journal = "The Analyst", volume = "5", pages = "53--54", kwds = "regr,stat,tls" } @book{ahhu:83, author = "A. V. Aho and J. E. Hopcroft and J. D. Ullman", year = "1983", title = "Data Structures and Algorithms", publisher = "Addison-Wesley", address = "Reading, MA", kwds = "" } @article{aike:34, author = "A. C. Aiken", year = "1934", title = "On Least Squares and Linear Combinations of Observations", journal = "Proceedings of the Royal Society of Edinburgh, Sec. A", volume = "55", pages = "42--47", kwds = "regr,stat" } @article{ajje:84, author = "M. A. Ajiz and A. Jennings", year = "1984", title = "A Robust Incomplete {Choleski}-Conjugate Gradient Algorithm", journal = "Internat. J. Numer. Methods. Engrg.", volume = "20", pages = "949--966", kwds = "cg, precond" } al- @article{alfl:85, author = "M. Al-Baali and R. Fletcher", year = "1985", title = "Variational Methods for Non-linear Least Squares", journal = "J. Oper. Res. Soc.", volume = "36", pages = "405--421", kwds = "nlsq" } @article{alfl:86, author = "M. Al-Baali and R. Fletcher", year = "1986", title = "An Efficient Line Search for Nonlinear Least-squares", journal = "J. Optim. Theory Appl.", volume = "48", pages = "359--377", kwds = "nlsq" } @phdthesis{alba:84, author = "M. Al-Baali", year = "1984", title = "Methods for Nonlinear Least Squares", school = "Department of Mathematical Sciences, University of Dundee", address = "Scotland", type = "{Ph. D.} thesis", kwds = "nlsq" } al- an- @article{alpp:88, author = "S. T. Alexander and C.-T. Pan and R. J. Plemmons", year = "1988", title = "Analysis of a Recursive Least Squares Hyperbolic Rotation Algorithm for Signal Processing", journal = "Linear Algebra Appl.", volume = "98", pages = "3-40", kwds = "downd, hyp, sigp, rls" } @article{alva:90, author = "F. L. Alvarado", year = "1990", title = "Manipulating and Visualization of Sparse Matrices", journal = "ORSA J. Comput.", volume = "2", pages = "186--207", kwds = "sparse, soft" } @phdthesis{ames:91, author = "P. R. Amestoy", year = "1991", title = "Factorization of Large Sparse Matrices Based on a Multifrontal Approach in a Multiprocessor Environment", school = "CERFACS", address = " Toulouse, France", type = "{Ph. D.} thesis", number = "TH/PA/91/2", kwds = "sparse, prll, thesis" } @article{amdu:89, author = "P. R. Amestoy and I. S. Duff", year = "1989", title = "Vectorization of a Multiprocessor Multifrontal Code", journal = "Internat. J. Supercomp. Appl.", volume = "3", pages = "41--59", kwds = "sparse, prll" } @article{amdu:93, author = "P. R. Amestoy and I. S. Duff", year = "1993", title = "Memory Allocation Issues in Sparse Multiprocessor Multifrontal Methods", journal = "Internat. J. Supercomput. Appl.", volume = "7", pages = "64--82", kwds = "sparse, prll" } @article{anpa:94, author = "A. A. Anda and H. Park", year = "1994", title = "Fast Plane Rotations with Dynamic Scaling", journal = " SIAM J. Matrix Anal. Appl.", volume = "15", pages = "162--174", kwds = "rot" } @article{anpa:96, author = "A. A. Anda and H. Park", year = "1996", title = "Self-Scaling Fast Rotations for Stiff Least Squares Problems", journal = "Linear Algebra Appl.", volume = "234", pages = "137--162", kwds = "rot, qrd,wlsq,constr" } @book{anbb:95, editor = "E. Anderson and Z. Bai and C. Bischof and J. Demmel and J. Dongarra and J. {Du Croz} and A. Greenbaum and S. Hammarling and A. McKenney and S. Ostrouchov and D. Sorensen ", year = "1995", title = "{LAPACK} Users' Guide. Second Edition", publisher = "SIAM", address = "Philadelphia", kwds = "prll,soft" } @book{anbb:99, editor = "E. Anderson and Z. Bai and C. Bischof and J. Demmel and J. Dongarra and J. {Du Croz} and A. Greenbaum and S. Hammarling and A. McKenney and D. Sorensen", year = "1999", title = "{LAPACK} Users' Guide. Third Edition", publisher = "SIAM", address = "Philadelphia", note={www.netlib.org/lapack/lug/lapack\_lug.html}, kwds = "prll,soft" } @techreport{anbd:91, author = "E. Anderssen and Z. Bai and J. Dongarra", title = "Generalized {QR} Factorization and its Applications", institution = "Computer Science Department", year = "1991", type = "{Tech. Report}", number = "CS-91-131", address = "University of Tennessee, Knoxville, TN", kwds = "iter" } @article{anka:75, author = "N. Anderson and I. Karasalo", year = "1975", title = "On Computing Bounds for the Least Singular Value of a Triangular Matrix", journal = "BIT", volume = "15", pages = "1--4", kwds = "err, rank, svd" } @techreport{ango:72, author = "R. S. Anderssen and G. Golub", title = "Richardson's Non-Stationary Matrix Iterative Procedure", institution = "Computer Science Department", year = "1972", type = "{Tech. Report}", number = "STAN-CS-72-304", address = "Stanford University, CA", kwds = "iter" } ar- as- @article{ardd:89, author = "M. Arioli and J. Demmel and I. S. Duff", year = "1989", title = "Solving Sparse Linear Systems with Sparse Backward Error", journal = " SIAM J. Matrix Anal. Appl.", volume = "10", pages = "165--190", kwds = "sparse, pert" } @article{ardr:89, author = "M. Arioli and I. S. Duff and P. P. M. de Rijk", year = "1989", title = "On the augmented system approach to sparse least-squares problems", journal = "Numer. Math.", volume = "55", pages = "667--684", kwds = "sparse, augms" } @article{ardr:92, author = "M. Arioli and I. S. Duff and D. Ruiz", year = "1992", title = "Stopping Criteria for Iterative Solvers", journal = " SIAM J. Matrix Anal. Appl.", volume = "13", pages = "138--144", kwds = "iter, pert" } @article{adrs:95, author = "M. Arioli and I. S. Duff and D. Ruiz and M. Sadkane", year = "1995", title = "Block {Lanczos} Techniques for Accelerating the Block {Cimmino} Method", journal = " SIAM J. Sci. Comput.", volume = "16", pages = "1478--1511", kwds = "iter, sparse, prll" } @article{ardn:92, author = "M. Arioli and I. S. Duff and J. Noailles and D. Ruiz", year = "1990", title = "A Block Projection Method for Sparse Matrices", journal = "SIAM J. Sci. Statist. Comput.", volume = "13", pages = "47--70", kwds = "sparse, iter" } @article{arla:86, author = "M. Arioli and A. Laratta", year = "1986", title = "Error analysis of an algorithm for solving an underdetermined linear system", journal = "Numer. Math.", volume = 46, pages = "255--268", kwds = "err, uds" } @article{arla:86a, author = "M. Arioli and A. Laratta", year = "1986", title = "Error analysis of algorithms for computing the projection of a Point onto a linear manifold", journal = "Linear Algebra Appl.", volume = 82, pages = "1--26", kwds = "uds, orth" } @article{asgr:89, author = "C. Ashcraft and R. G. Grimes", year = "1989", title = "The Influence of Relaxed Supernode Partitions on the Multifrontal Method", journal = "ACM Trans. Math. Software", volume = "15", pages = "291--309", kwds = "sparse, prll" } @techreport{ashc:87, author = "C. Ashcraft", year = "1987", title = "A Vector Implementation of the Multifrontal Method for Large Sparse Positive definite Systems", institution = "Engineering Technology Division, Boeing Computer Services", address= "Seattle, WA", type = "{Tech. Report}", number = "ETA-TR-51", kwds = "sparse, prll" } @incollection{ashk:71, author = "V. Ashkenazi", year = "1971", title = " Geodetic Normal Equations", booktitle = "Large Sets of Linear Equations", editor = "J. K. Reid", pages = "57--74", publisher = "Academic Press, New York", kwds = "geod, ne" } av- @inproceedings{avto:79, author = "J. K. Avila and J. A. Tomlin", year = "1979", title = "Solution of Very Large Least Squares Problems by Nested Dissection on a Parallel Processor", booktitle = "Proceedings of the Computer Science and Statistics 12th Annual Symposium on the Interface", editor = "J. F. Gentleman", publisher = "University of Waterloo, Canada", kwds = "sparse, perm" } ba- @techreport{bai:92, author = "Z. Bai", year = "1992", title = "The {CSD}, {GSVD}, Their Applications and Computations", institution = "Institute for Mathematics and Its Applications, University of Minnesota", address = "Minneapolis, MN", type = "{Tech. Report}", number = "IMA Preprint Series 958", kwds = "csd, gsvd" } @article{bade:93, author = "Z. Bai and J. W. Demmel", year = "1993", title = "Computing the Generalized Singular Value Decomposition", journal = "SIAM J. Sci. Comput.", volume = "14", pages = "1464--1486", kwds = "gsvd" } @article{bazh:93, author = "Z. Bai and H. Zha", year = "1993", title = "A New Preprocessing Algorithm for the Computation of the Generalized Singular Value Decomposition", journal = "SIAM J. Sci. Comput.", volume = "14", pages = "1007--1012", kwds = "gqrd, gsvd" } @article{bana:38, author = "T. Banachiewicz", year = "1938", title = "Principes d'une nouvelle technique de la m\'ethode des moindres carr\'es", journal = "Bull. Internat. Acad. Polon. Sci. A", pages = "134--135", kwds = "chol" } @book{bard:74, author = "Y. Bard", year = "1974", title = "Nonlinear Parameter Estimation", publisher = "Academic Press", address = "New York", kwds = "stat, nlsq" } @techreport{bare:82, author = "E. H. Bareiss", year = "1982", title = "Numerical Solution of the Weighted Linear Least Squares Problems by {G}-transformations", institution = "Department of Electrical Engineering and Computer Science", address = "Northwestern University, Evanston, IL", type = "{Tech. Report}", number = "82-03-NAM-03", kwds = "wlsq" } @article{barl:85, author = "J. L. Barlow", year = "1985", title = "Stability Analysis of the {G}-algorithm and a Note on its Application to Sparse Least Squares Problems", journal = "BIT", volume = "25", pages = "507--520", kwds = "wlsq" } @article{barl:88, author = "J. L. Barlow", year = "1988", title = "Error Analysis and Implementation Aspects of Deferred Correction for Equality Constrained Least Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "25", pages = "1340--1358", kwds = "constr, err" } @techreport{barl:89, author = "J. L. Barlow", year = "1989", title = "The Accurate Solution of Sparse Weighted and Equality Constrained Least Squares Problems Using a Static Data Structure", institution = "Dept. of Computer Science, The Pennsylvania State University", address = "State College, PA", type = "{Tech. Report}", number = "CS-89-03", kwds = "wlsq, constr,sparse" } @article{barl:90, author = "J. L. Barlow", year = "1990", title = "On the Use of Structural Zeros in Orthogonal Factorization", journal = "SIAM J. Sci. Stat. Comput.", volume = "11", pages = "600--601", kwds = "constr, err" } @article{baha:88, author = "J. L. Barlow and S. L. Handy", year = "1988", title = "The Direct Solution of Weighted and Equality Constrained Least Squares Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "9", pages = "704--716", kwds = "wlsq, constr" } @article{baip:87, author = "J. L. Barlow and I. C. F. Ipsen", year = "1987", title = "Scaled {Givens} Rotations for the Solution of Linear Least Squares Problems on Systolic Arrays", journal = "SIAM J. Sci. Statist. Comput.", volume = "8", pages = "716-734", kwds = "prll, rot" } @article{banp:88, author = "J. L. Barlow and N. K. Nichols and R. J. Plemmons", year = "1988", title = " Iterative Methods for Equality-constrained Least Squares Problems.", journal = "SIAM J. Sci. Statist. Comput.", volume = "9", pages = "892--906", kwds = "iter, constr" } @article{bave:92, author = "J. L. Barlow and U. B. Vemulapati", year = "1992", title = "Rank Detection Methods for Sparse Matrices", journal = "SIAM J. Matrix Anal. Appl.", volume = "13", pages = "1279--1297", kwds = "rank, rrqrd, sparse" } @article{bayz:96, author = "J. L. Barlow and P. A. Yoon and H. Zha", year = "1996", title = "An Algorithm and a Stability Theory for Downdating the {ULV} Decomposition", journal = "BIT", volume = "36", pages = "14--40", kwds = "upd, rrqrd, svd" } @techreport{bazy:93, author = "J. L. Barlow and H. Zha and P. A. Yoon", year = "1993", title = "Stable Chasing Algorithms for Modifying Complete and Partial Singular Value Decompositions", institution = "Department of Computer Science", address = "The Pennsylvania State University, State College, PA", type = "{Tech. Report}", number = "CSE-93-19", kwds = "upd, svd" } @book{babc:93, editor = "R. Barret and M. W. Berry and T. Chan and J. Demmel and J. Donato and J. Dongarra and V. Eijkhout and R. Pozo and C. Romine and H. van der Vorst", year = "1993", title = "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods ", publisher = "SIAM", address = "Philadelphia", kwds = "iter, survey" } @article{barr:94, author = "A. Barrlund", year = "1994", title = "Perturbation Bounds for the Generalized {QR} Factorization", journal = "Linear Algebra Appl.", volume = "207", pages = "251--272", kwds = "pert, qrd" } @article{baro:73, author = "I. Barrodale and F. D. K. Roberts", year = "1973", title = "An Improved Algorithm for Discrete $\ell_1$ Linear Approximation", journal = "SIAM J. Numer. Anal.", volume = "10", pages = "839--848", kwds = "rob" } @article{baph:75, author = "I. Barrodale and C. Phillips", year = "1975", title = "Algorithm {\rm 495}: Solution of an Overdetermined System of Linear Equations in the {Chebyshev} Norm ", journal = "ACM Trans. Math. Software", volume = "1", pages = "264--270", kwds = "cheb" } @article{baro:78, author = "I. Barrodale and F. D. K. Roberts", year = "1978", title = "An Efficient Algorithm for Discrete $\ell_1$ Linear Approximation with Linear Constraints", journal = "SIAM J. Numer. Anal.", volume = "15", pages = "603--611", kwds = "rob" } @incollection{bags:70, author = "R. H. Bartels and G. H. Golub and M. A. Saunders", year = "1970", title = "Numerical Techniques in Mathematical Programming", pages = "123--176", booktitle = "Nonlinear Programming", editor = "J. B. Rosen and O. L. Mangasarian and K. Ritter", publisher = "Academic Press, New York", kwds = "qrd, rank" } @article{baco:80, author = "R. H. Bartels and A. R. Conn", year = "1980", title = "Linearly Constrained Discrete $\ell_1$ Problems", journal = "ACM Trans. Math. Software", volume = "6", pages = "594--608", kwds = "rob, constr" } @article{bacc:80, author = "R. H. Bartels and A. R. Conn and C. Charalambous", year = "1980", title = "On {Cline's} Direct Method for Solving Overdetermined Linear Systems in the {$\ell_\infty$} Sense", journal = " SIAM J. Numer. Anal.", volume = "15", pages = "255--270", kwds = "cheb" } @article{bacs:78, author = "R. H. Bartels and A. R. Conn and J. W. Sinclair", year = "1978", title = "Minimization Techniques for Piecewise Differentiable Functions: The $\ell_1$ Solution to an Overdetermined Linear System", journal = "SIAM J. Numer. Anal.", volume = "15", pages = "224--241", kwds = "rob" } @article{bamw:67, author = "W. Barth and R. S. Martin and J. H. Wilkinson", year = "1967", title = "Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection", journal = "Numer. Math.", volume = "9", pages = "386--393", kwds = "svd" } @article{baue:65, author = "F. L. Bauer", year = "1965", title = "Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems", journal = "Numer. Math.", volume = "7", pages = "338--352", kwds = "grsch, qrd" } @article{baue:66, author = "F. L. Bauer", year = "1966", title = " {Genauigkeitsfragen bei der L{\"o}sung linear Gleich\-ungs\-systeme}", journal = "{Z. Angew. Math. Mech.}", volume = "46", pages = "409--421", kwds = "pert, cond, scale" } be- @article{biwe:63, author = "A. Ben-Israel and S. J. Wersan", year = "1963", title = "An Elimination Method for Computing the generalized Inverse of an Arbitrary Matrix", journal = "J. ACM", volume = "10", pages = "532--537", kwds = "ginv" } @article{beno:24, author = "Benoit, Commendant", year = "1924", title = "Sur la m\'ethode de r\'esolution des \'equationes normales, etc. (Proc\'ed\'es du commandant {Cholesky})", journal = "Bull. G\'eod\'esique", volume = "2", pages = "67--77", kwds = "chol, ne" } @article{tate:90, author = "A. Ben-Tal and M. Teboulle", year = "1990", title = "A Geometric Property of the Least Squares Solution of Linear Equations", journal = "Linear Algebra Appl.", volume = "139", pages = "165--170", kwds = "wlsq" } @phdthesis{benz:93, author = "M. Benzi", year = "1993", title = "A Direct Row-Projection Method for Sparse Linear Systems", school = "North Carolina State University", address = "Raleigh, NC", type = "{Ph. D.} thesis", kwds = "iter" } @inproceedings{beme:94, author = "M. Benzi and C. D. Meyer", year = "1994", title = "An Explicit Preconditioner for the Conjugate Gradient Method", booktitle = "Proceedings of the {Cornelius} Lanczos International Centenary Conference, Raleigh, NC, Dec. 1993", editor = "J. D. Brown and M. T. Chu and D. C. Ellison and R. J. Plemmons", publisher = "SIAM, Philadelphia", pages = "294--296", kwds = "precond, cg" } @article{bemt:96, author = "M. BENZI and C.D. MEYER and M. T\.{U}MA", title = "A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method", journal = "SIAM J. Sci. Comput.", volume = "17", number = "5", pages = "1135-1149", year = "1996", kwds = "precond, cg" } @article{bemt:98, author = "M. BENZI and M. T\.{U}MA", year = "1998", title = "A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems", journal = "SIAM J. Sci. Comput.", volume = "19", number = "3", pages = "968-994", kwds = "precond, cg" } @article{bepl:74, author = "A. Berman and R. J. Plemmons", year = "1974", title = "Cones and Iterative Methods for Best Least Squares Solutions of Linear Systems", journal = "SIAM J. Numer. Anal.", volume = "11", pages = "145--154", kwds = "iter" } @article{berr:92, author = "M. W. Berry", year = "1992", title = "Large Scale Sparse Singular Value Computations", journal = "Internat. J. Supercomp. Appl.", volume = "6", pages = "13--49", kwds = "sparse, svd" } @techreport{berr:92b, author = "M. W. Berry", year = "1992", title = "A {Fortran}-{\rm 77} Software Library for the Sparse Singular Value Decomposition", institution = "University of Tennessee", address = "Knoxville, TN", type = "{Tech. Report}", number = "CS-92-159", kwds = "sparse, svd, soft" } @techreport{berr:93, author = "M. W. Berry", year = "1993", title = "{SVDPACKC}: Version {\rm 1.0} User's Guide", institution = "University of Tennessee", address = "Knoxville, TN", type = "{Tech. Report}", number = "CS-93-194", kwds = "sparse, svd" } @inproceedings{berr:94, author = "M. W. Berry", year = "1994", title = "A Survey of Public-Domain {Lanczos}-Based Software", booktitle = "Proceedings of the {Cornelius} {Lanczos} International Centenary Conference, Raleigh, NC, Dec. 1993", editor = "J. D. Brown and M. T. Chu and D. C. Ellison and R. J. Plemmons", publisher = "SIAM, Philadelphia", pages = "332--334", kwds = "iter, lancz" } @inproceedings{beau:94, author = "M. W. Berry and R. L. Auerbach", year = "1994", title = "A Block {Lanczos} {SVD} Method with Adaptive Reorthogonalization", booktitle = "Proceedings of the {Cornelius} {Lanczos} International Centenary Conference, Raleigh, NC, Dec. 1993", editor = "J. D. Brown and M. T. Chu and D. C. Ellison and R. J. Plemmons", publisher = "SIAM, Philadelphia", pages = "329--331", kwds = "iter, lancz" } @article{bego:91, author = "M. W. Berry and G. H. Golub", year = "1991", title = "Estimating the Largest Singular Values of Large Sparse Matrices via Modified Moments", journal = "Numer. Algorithms", volume = "1", pages = "363--374", kwds = "sparse, svd" } @article{bert:1855, author = "J. Bertrand", year = "1855", title = "Sur la m\'ethode des moindres carr\'es", journal = "C. R. Acad. Sci., Paris", volume = "40", pages = "1190--1192", kwds = "ne, hist" } bi- @article{bien:1853, author = "I. J. Bienaym\'e", year = "1853", title = "Remarques sur les diff\'erences qui distinguent l'interpolation de {M. Cauchy} de la m\'ethode des moindre carr\'es et qui assurent la sup\'eriorit\'e de cette m\'ethode", journal = "C. R. Acad. Sci., Paris", volume = "37", pages = "5--13", kwds = "ne, hist" } @article{bitt:91, author = "M. Bierlair and P. Toint and D. Tuyttens", year = "1991", title = "On Iterative Algorithms for Linear Least-Squares Problems with Bound Constraints", journal = "Linear Algebra Appl.", volume = "143", pages = "111-143", kwds = "iter, constr" } @inproceedings{bisc:89, author = "C. H. Bischof", year = "1989", title = "A Block {QR} Factorization Algorithm Using Restricted Pivoting", pages = "248--256", booktitle = "Supercomputing 89", editor = "", publisher = "ACM Press, New York", kwds = "qrd, prll, blas" } @article{bisc:90, author = "C. H. Bischof", year = "1990", title = "Incremental Condition Estimation", journal = "SIAM J. Matrix Anal. Appl.", volume = "11", pages = "312--322", kwds = "cond" } @techreport{bisc:90a, author = "C. H. Bischof", year = "1990", title = "Adaptive Condition Estimation for Rank-one Downdates of {QR} Factorizations", institution = "Argonne National Laboratory, Math. and Computer Sciences Div.", address = "Argonne, IL", type = "{Tech. Report}", number = "ANL/MCS-P166-0790", kwds = "cond" } @article{bisc:91, author = "C. H. Bischof", year = "1991", title = "A Parallel {QR} Factorization Algorithm with Controlled Local Pivoting", journal = "SIAM J. Sci. Statist. Comput.", volume = "12", pages = "36--57", kwds = "cond" } @article{biha:91, author = "C. H. Bischof and P. C. Hansen", year = "1991", title = "Structure Preserving and Rank-Revealing {QR} Factorizations", journal = "SIAM J. Sci. Statist. Comput.", volume = "12", pages = "1332--1350", kwds = "sparse, rrqrd" } @article{biha:92, author = "C. H. Bischof and P. C. Hansen", year = "1992", title = "A Block Algorithm for Computing Rank-Revealing {QR} Factorizations", journal = "Numer. Algorithms", volume = "2", pages = "371--392", kwds = "cond,rrqrd" } @article{bilp:90, author = "C. H. Bischof and J. G. Lewis and D. J. Pierce", year = "1990", title = "Incremental Condition Estimation for Sparse Matrices", journal = "SIAM J. Matrix Anal. Appl.", volume = "11", pages = "644--659", kwds = "sparse, cond, err" } @article{bipt:93, author = "C. H. Bischof and C.-T. Pan and P. T. P. Tang", year = "1993", title = "A {Cholesky} Up-and Downdating Algorithm for Systolic and {SIMD} Architectures", journal = "SIAM J. Sci. Comput.", volume = "14", pages = "670--676", kwds = "downd, prll" } bj- @article{bjer:51, author = "A. Bjerhammer", year = "1951", title = "Rectangular Reciprocal Matrices with Special Reference to Geodetic Calculations", journal = "Bull. G\'eod\'esique", volume = "52", pages = "118-220", kwds = "ginv" } @article{bjor:67, author = "{\AA}. Bj{\"o}rck", year = "1967", title = "Solving Linear Least Squares Problems by {Gram-Schmidt} Orthogonalization", journal = "BIT", volume = "7", pages = "1--21", kwds = "qrd, grsch" } @article{bjor:67a, author = "{\AA}. Bj{\"o}rck", year = "1967", title = "Iterative Refinement of Linear Least Squares Solutions {I}", journal = "BIT", volume = "7", pages = "257--278", kwds = "ir, grsch, qrd" } @article{bjor:68, author = "{\AA}. Bj{\"o}rck", year = "1968", title = "Iterative Refinement of Linear Least Squares Solutions {II}", journal = "BIT", volume = "8", pages = "8-30", kwds = "ir, constr" } @inproceedings{bjor:76, author = "{\AA}. BJ{\"O}RCK", year = "1976", title = "Methods for Sparse Least Squares Problems", pages = "177--199", booktitle = "Sparse Matrix Computations", editor = "J.R. Bunch and D. J. Rose", publisher = "Academic Press, New York", kwds = "sparse, survey" } @article{bjor:78, author = "{\AA}. Bj{\"o}rck", year = "1978", title = "Comment on the Iterative Refinement of Least Squares Solutions", journal = "J. Amer. Statist. Assoc.", volume = "73", pages = "161--166", kwds = "ir, sne" } @inproceedings{bjor:79, author = "{\AA}. Bj{\"o}rck", year = "1979", title = "{SSOR} Preconditioning Methods for Sparse Least Squares Problems", pages = "21--25", booktitle = "Proceedings of the Computer Science and Statistics 12th Annual Symposium on the Interface", editor = "J. F. Gentleman", publisher = "University of Waterloo, Canada", kwds = "iter, precond" } @article{bjor:84, author = "{\AA}. Bj{\"o}rck", year = "1984", title = "A General Updating Algorithm for Constrained Linear Least Squares problems", journal = " SIAM J. Sci. Statist. Comput.", volume = "5", pages = "394--402.", kwds = "upd, sparse" } @article{bjor:87, author = "{\AA}. Bj{\"o}rck", year = "1987", title = "Stability Analysis of the Method of Semi-Normal Equations for Least Squares Problems", journal = "Linear Algebra Appl.", volume = "88/89", pages = "31--48", kwds = "err, ne" } @article{bjor:88, author = "{\AA}. Bj{\"o}rck", year = "1988", title = "A Bidiagonalization Algorithm for Solving Ill-posed Systems of Linear Equations", journal = "BIT", volume = "28", pages = "659--670", kwds = "sparse, lanczos" } @article{bjor:88a, author = "{\AA}. Bj{\"o}rck", year = "1988", title = "A Direct Method for Sparse Least Squares Problems with lower and Upper Bounds", journal = " Numer. Math.", volume = "54", pages = "19--32", kwds = "constr" } @inproceedings{bjor:90b, author = "{\AA}. Bj{\"o}rck", year = "1990", title = "Iterative Refinement and Reliable Computing", pages = "249--266", booktitle = "Reliable Numerical Computation", editor = "M. G. Cox and S. J. Hammarling", publisher = "Clarendon Press, Oxford, UK", kwds = "" } @incollection{bjor:90c, author = "{\AA}. BJ{\"O}RCK", year = "1990", title = "Least Squares Methods", editor = "P. G. Ciarlet and J. L. Lions", booktitle = "Handbook of Numerical Analysis. I. Solution of Equations in $R^n$. Part 1", publisher = "Elsevier/North-Holland, Amsterdam", pages = "466--647", kwds = "survey" } @inproceedings{bjor:91, author = "{\AA}. Bj{\"o}rck", year = "1991", title = "Error Analysis of Least Squares Algorithms", pages = "41--73", booktitle = "Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms", series = "NATO ASI Series", volume = "70", editor = "G. H. Golub and P. {Van Dooren}", publisher = "Springer-Verlag, Berlin", kwds = "err, sigp" } @article{bjor:91a, author = "{\AA}. Bj{\"o}rck", year = "1991", title = "Component-wise Perturbation Analysis and Errors Bounds for Linear Least Square Solutions", journal = "BIT", volume = "31", pages = "238--244", kwds = "pert, pert" } @inproceedings{bjor:91b, author = "{\AA}. Bj{\"o}rck", year = "1991", title = "Algorithms for Linear Least Squares Problems", pages = "57--92", booktitle = "Computer Algorithms for Solving Linear Algebraic Equations; The State of the Art", series = "NATO ASI Series F: Computer and Systems Sciences", volume = "77", editor = "E. Spedicato", publisher = "Springer-Verlag, Berlin", kwds = "survey" } @inproceedings{bjor:92, author = "{\AA}. Bj{\"o}rck", year = "1992", title = "Pivoting and Stability in the Augmented System Method", pages = "1--16", booktitle = "Numerical Analysis 1991: Proceedings of the 14th Dundee Conference, June 1991", editor = "D. F. Griffiths and G. A. Watson", publisher = "Longman Scientific and Technical, Harlow, UK", series = "Pitman Research Notes in Mathematics 260", kwds = "augms, err, wlsq" } @article{bjor:94, author = "{\AA}. Bj{\"o}rck", year = "1994", title = "Numerics of {Gram-Schmidt} Orthogonalization", journal = "Linear Algebra Appl.", volume = "197--198", pages = "297--316", kwds = "survey, grsch" } @inproceedings{bjor:94a, author = "{\AA}. Bj{\"o}rck", year = "1994", title = "Generalized and Sparse Least Squares Problems", pages = "37--80", booktitle = "Algorithms for Continuous Optimization; The State of the Art", series = "NATO ASI Series C: Mathematical and Physical Sciences", volume = "434", editor = "E. Spedicato", publisher = "Kluwer Academic Publisher, Dordrecht", kwds = "survey" } @book{bjor:96, author = "{\AA}. Bj{\"o}rck", year = "1996", title = " Numerical Methods for Least Squares Problems", publisher = "SIAM", address = "Philadelphia", kwds = "survey" } @book {MR97g:65004, AUTHOR = {Bj{\"o}rck, {\AA}ke}, TITLE = {Numerical methods for least squares problems}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1996}, PAGES = {xviii+408}, ISBN = {0-89871-360-9}, MRCLASS = {65-02 (65Fxx 65H99)}, MRNUMBER = {97g:65004}, MRREVIEWER = {Hongyuan Zha}, } @article{bjbo:71, author = "{\AA}. Bj{\"o}rck and C. Bowie", year = "1971", title = "An Iterative Algorithm for Computing the Best Estimate of an Orthogonal Matrix", journal = "SIAM J. Numer. Anal.", volume = "8", pages = "358--364", kwds = "svd, orth, iter" } @article{bjdu:80, author = "{\AA}. {Bj{\"o}rck} and I. S. Duff", year = "1980", title = "A Direct Method for the Solution of Sparse Linear Least Squares Problems", journal = "Linear Algebra Appl.", volume = "34", pages = "43-67", kwds = "ne, lud, sparse" } @techreport{bjel:79, author = "{\AA}. Bj{\"o}rck and L. Eld\'en", year = "1979", title = "Methods in numerical algebra for ill-posed problems", institution = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", type = "{Tech. Report}", number = "LiTH-MAT-R-1979-33", kwds = "regul" } @article{bjep:94, author = "{\AA}. Bj{\"o}rck and L. Eld\'en and H. Park", year = "1994", title = "Accurate Downdating of Least Squares Solutions", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "549--568", kwds = ",sne, downd" } @article{bjel:73, author = "{\AA}. Bj{\"o}rck and T. Elfving", year = "1973", title = "Algorithms for Confluent {Vandermonde} Systems", journal = "Numer. Math.", volume = "21", pages = "130--137", kwds = "vand" } @article{bjelf:79, author = "{\AA}. BJ{\"O}RCK and T. ELFVING", year = "1979", title = "Accelerated Projection Methods for Computing Pseudoinverse Solutions of Systems of Linear Equations", journal = "BIT", volume = "19", pages = "145--163", kwds = "ginv, iter, prll" } @techreport{bjes:95, author = "{\AA}. Bj{\"o}rck and T. Elfving and Z. Strakos", year = "1995", title = "Implementing Conjugate Gradient-Type Methods for Linear Least Squares Problems", institution = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", type = "{Tech. Report}", number = "LiTH-MAT-R-95-26", kwds = "cg, iter" } @article{bjgo:67, author = "{\AA}. Bj{\"o}rck and G. H. Golub", year = "1967", title = "Iterative Refinement of Linear Least Squares Solution by {Householder} Transformation", journal = "BIT", volume = "7", pages = "322--337", kwds = "ir, qrd" } @article{bjgo:73, author = "{\AA}. Bj{\"o}rck and G. H. Golub", year = "1973", title = "Numerical Methods for Computing Angles between Linear Subspaces", journal = "Math. Comp.", volume = "27", pages = "579--594", kwds = "csd" } @article{bjgv:94, author = "{\AA}. Bj{\"o}rck and E. Grimme and P. {Van Dooren}", year = "1994", title = "An Implicit Bidiagonalization Algorithm for Ill-Posed Systems", journal = "BIT", volume = "34", pages = "510--534", kwds = "regul, illp, lanczos" } @book{bjps:81, editor = "{\AA}. Bj{\"o}rck and R. J. Plemmons and H. Schneider", year = "1981", title = "Large Scale Matrix Problems", publisher = "North-Holland, New York", kwds = "sparse, survey" } @article{bjpa:92, author = "{\AA}. Bj{\"o}rck and C. C. Paige", year = "1992", title = "Loss and Recapture of Orthogonality in the Modified {Gram-Schmidt} Algorithm", journal = "SIAM J. Matrix Anal. Appl.", volume = "13", pages = "176--190", kwds = "qrd, grsch" } @article{bjpa:94, author = "{\AA}. Bj{\"o}rck and C. C. Paige", year = "1994", title = "Solution of Augmented Linear Systems using Orthogonal Factorizations", journal = "BIT", volume = "34", pages = "1--26", kwds = "qrd, grsch, augms" } @article{bjpe:70, author = "{\AA}. Bj{\"o}rck and V. Pereyra", year = "1970", title = "Solution of {Vandermonde} System of Equations", journal = "Math. Comp.", volume = "24", pages = "893--903", kwds = "vand" } bl- @article{blue:78, author = "J. L. Blue", year = "1978", title = "A Portable {Fortran} Program to Find the {Euclidean} Norm of a Vector", journal = "Trans. Math. Software", volume = "4", pages = "15-23", kwds = "blas, soft" } bo- @article{bobs:87, author = "P. T. Boggs and R. H. Byrd and R. B. Schnabel", year = "1987", title = "A Stable and Efficient Algorithm for Nonlinear Orthogonal Regression", journal = " SIAM J. Sci. Statist. Comput.", volume = "8", pages = "1052--1078", kwds = "nlsq, regr" } @techreport{bobr:92, author = "P. T. Boggs and R. H. Byrd and J. E. Rogers and R. B. Schnabel", year = "1992", title = "User's Reference Guide for {ODRPACK} Version {\rm 2.01}---{Software} for Weighted Orthogonal Distance Regression", institution = "National Institute of Standards and Technology", address = "Gaithersburg, MD", number = "LiTH-MAT-R-1979-33", kwds = "nlsq, regr" } @article{bobr:86, author = "A. W. Bojanczyk and R. P. Brent", year = "1986", title = "Parallel Solution of Certain {Toeplitz} Least-Squares Problems", journal = "Linear Algebra Appl.", volume = "77", pages = "43-60", kwds = "prll, toep" } @article{bobh:86, author = "A.~W. Bojanczyk and R. P. Brent and F.~R. de Hoog", year = "1986", title = "{QR} Factorization of {Toeplitz} Matrices", journal = "Numer. Math.", volume = "49", pages = "81--94", kwds = "qrd, toep" } @techreport{bobh:93, author = "A.~W. Bojanczyk and R. P. Brent and F.~R. de Hoog", year = "1993", title = "A Weakly Stable Algorithm for General {Toeplitz} Matrices", institution = "Cornell University", address = "Ithaca, NY", type = "{Tech. Report}", number = "TR-CS-93-15", kwds = "qrd, toep" } @article{bobv:87, author = "A. W. Bojanczyk and R. P. Brent and P. {Van Dooren} and F. de Hoog", year = "1987", title = "A Note on Downdating the {Cholesky} Factorization", journal = "SIAM J. Sci. Statist. Comput.", volume = "8", pages = "210--221", kwds = "down, chol" } @article{bonp:93, author = "A. W. Bojanczyk and J. G. Nagy and R. J. Plemmons", year = "1993", title = "Block {RLS} Using Row {Householder} Reflections", journal = "Linear Algebra Appl.", volume = "188/189", pages = "31--62", kwds = "upd, house, sigp" } @inproceedings{bole:94, author = "A.~W. Bojanczyk and J. M. Lebak", year = "1994", title = "Downdating a {ULLV} Decomposition of Two Matrices", editor = "J. G. Lewis", booktitle = "Proceedings of the Fifth SIAM Conference on Applied Linear Algebra", pages = "261--265", publisher = "SIAM, Philadelphia", kwds = "gqrd, downd" } @article{bogo:87, author = "D. Boley and G. H. Golub", year = "1987", title = "A Survey of Matrix Inverse Eigenvalue Problems", journal = "Inverse Problems", volume = "3", pages = "595--622", kwds = "eigv" } @article{book:79, author = "F. L. Bookstein", year = "1979", title = "Fitting Conic Sections to Scattered Data", journal = "Computer Graphics and Image Processing", volume = "9", pages = "56--71", kwds = "geom, nlsq" } @book{boor:78, author = "C. de BOOR", year = "1978", title = "A Practical Guide to Splines", publisher = "Springer-Verlag", address = "Berlin", kwds = "spline" } @book{boor, author = "C. de BOOR", year = "1978", title = "A Practical Guide to Splines", publisher = "Springer-Verlag", address = "Berlin", kwds = "spline" } @article{boko:95, author = "T. Boros and T. Kailath and V. Olshevsky", year = "1995", title = "Error Analysis of a Fast Algorithm for Solving {Cauchy} Linear Systems", note = "submitted", journal = "", volume = "", pages = "", kwds = "" } br- @phdthesis{bram:89, author = "R. Bramley", year = "1989", title = "Row-Projection Methods for Linear Systems", school = "Center for Supercomputing Research and Development, University of Illinois", address = "Urbana, IL", type = "{Ph. D.} thesis 881", kwds = "iter" } @article{brsa:92, author = "R. Bramley and A. Sameh", year = "1992", title = "Row Projection Methods for Large Nonsymmetric Linear Systems", journal = "SIAM J. Sci. Statist. Comput.", volume = "13", pages = "168--193", kwds = "iter, sparse, prll" } @inproceedings{bren:88, author = "R. P. Brent", year = "1988", title = "Old and New Algorithms for {Toeplitz} Systems", editor = "Franklin T. Luk", booktitle = "Advanced Algorithms and Architectures for Signal Processing III", pages = "2--9", series = "SPIE Proceeding Series, Washington", kwds = "survey, toep" } bu- @article{bunc:71, author = "J. R. Bunch", year = "1971", title = "Analysis of the Diagonal Pivoting Method", journal = "SIAM J. Numer. Anal.", volume = "8", pages = "656--680", kwds = "augms" } @article{bunc:85, author = "J. R. Bunch", year = "1985", title = "Stability of Methods for Solving {Toeplitz} Systems of Equations", journal = "SIAM J. Sci. Statist. Comput.", volume = "6", pages = "349--364", kwds = "toep" } @article{bunc:87, author = "J. R. Bunch", year = "1987", title = "The Weak and Strong Stability of Algorithms in Numerical Linear Algebra", journal = "Linear Algebra Appl.", volume = "88/89", pages = "49--66", kwds = "pert, err" } @article{budv:89, author = "J. R. Bunch and J. W. Demmel and C. F. {Van Loan}", year = "1989", title = "The Strong Stability of Algorithms for Solving Symmetric Systems", journal = "SIAM J. Matrix Anal. Appl.", volume = "10", pages = "494--499", kwds = "pert, err" } @article{bupa:71, author = "J. R. Bunch and B. N. Parlett", year = "1971", title = "Direct Methods for Solving Symmetric Indefinite Systems of Linear Systems", journal = "SIAM J. Numer. Anal.", volume = "8", pages = "639--655", kwds = "augms" } @article{buka:77, author = "J. R. Bunch and L. Kaufman", title = "Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems", year = "1977", journal = "Math. Comp.", volume = "31", pages = "162--179", kwds = "augms" } @article{bukp:76, author = "J. R. Bunch and L. Kaufman and B. N. Parlett", year = "1976", title = "Decomposition of a Symmetric Matrix", journal = "Numer. Math.", volume = "27", pages = "95--109", kwds = "augms" } @article{buni:78, author = "J. R. Bunch and C. P. Nielsen", year = "1978", title = "Updating the Singular Value Decomposition", journal = "Numer. Math.", volume = "31", pages = "111--129", kwds = "upd, svd" } @proceedings{buro:76, editor = "J. R. Bunch and D. J. Rose", year = "1976", title = "Sparse Matrix Computations", publisher = "Academic Press, New York", kwds = "sparse, survey" } @article{busi:70, author = "P. Businger", year = "1970", title = "Updating a Singular Value Decomposition", journal = "BIT", volume = "10", pages = "376--385", kwds = "svd, upd" } @article{bugo:65, author = "P. Businger and G. H. Golub", year = "1965", title = "Linear Least Squares Solutions by {Householder} Transformations", journal = "Numer. Math.", volume = "7", pages = "269--276", kwds = "qrd, hist" } @article{bugo:69, author = "P. Businger and G. H. Golub", year = "1969", title = "Algorithm {\rm 358}: Singular Value Decomposition of a Complex Matrix", journal = "Comm. ACM ", volume = "12", pages = "564--565", kwds = "qrd, soft" } ca- ch- @article{care:93, author = "D. Calvetti and L. Reichel", year = "1993", title = "Fast Inversion of {Vandermonde}-like Matrices Involving Orthogonal Polynomials", journal = "BIT", volume = "33", pages = "473--484", kwds = "poly, vand" } @article{casc:63, author = "D. Carlson and H. Schneider", year = "1963", title = "Inertia Theorems for Matrices: {The} Positive Semidefinite Case", journal = "J. Math. Anal. Appl.", volume = "6", pages = "430--446", kwds = "augms" } @article{cauc:1837, author = "A. Cauchy", year = "1837", title = "M\'emoire sur l'Interpolation", journal = "J. Math. Pures Appl.", volume = "2", pages = "193--205", kwds = "hist" } @article{cham:71, author = "J. M. Chambers", year = "1971", title = "Regression Updating", journal = "J. Amer. Statist. Assoc.", volume = "66", pages = "744--748", kwds = "upd, downd, stat, regr" } @book{cham:77, author = "J. M. Chambers", year = "1977", title = "Computational Methods for Data Analysis", publisher = "John Wiley", address = "New York", kwds = "stat, regr" } @article{chan:82, author = "T. F. Chan", year = "1982", title = "An Improved Algorithm for Computing the Singular Value Decomposition", journal = "ACM Trans. Math. Software", volume = "8", pages = "72--83", kwds = "svd" } @article{chan:82a, author = "T. F. Chan", year = "1982", title = "Algorithm {\rm 581}: An Improved Algorithm for Computing the Singular Value Decomposition", journal = "ACM Trans. Math. Software", volume = "8", pages = "84--88", kwds = "svd, soft" } @article{chan:87, author = "T. F. Chan", year = "1987", title = "Rank Revealing {QR}-factorizations", journal = "Linear Algebra Appl.", volume = "88/89", pages = "67--82", kwds = "qrd, rank, rrqrd" } @article{chha:90, author = "T. F. Chan and P. C. Hansen", year = "1990", title = "Computing Truncated {SVD} Least Squares Solutions by Rank Revealing {QR} Factorizations", journal = "SIAM J. Sci. Statist. Comput.", volume = "11", pages = "519--530", kwds = "qrd, rank, rrqrd" } @article{chha:92, author = "T. F. Chan and P. C. Hansen", year = "1992", title = "Some Applications of the Rank Revealing {QR} Factorization", journal = "SIAM J. Sci. Statist. Comput.", volume = "13", pages = "727--741", kwds = "tls, qrd, rank, rrqrd" } @article{chha:94, author = "T. F. Chan and P. C. Hansen", year = "1994", title = "Low-Rank Revealing {QR} Factorizations", journal = "Numer. Linear Algebra Appl.", volume = "1", pages = "33--44", kwds = "qrd, rank, rrqrd" } @article{chnp:93, author = "R. H. Chan and J. G. Nagy and R. J. Plemmons", year = "1993", title = "{FFT}-Based Preconditioners for {Toeplitz}-Block Least Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "30", pages = "1740--1768", kwds = "toep, cg, precond" } @article{chnp:94, author = "R. H. Chan and J. G. Nagy and R. J. Plemmons", year = "1994", title = "Circulant Preconditioned {Toeplitz} Least Squares Iterations", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "80--97", kwds = "toep, cg, precond" } @techreport{chip:92, author = "S. Chandrasekaran and I. C. F. Ipsen", year = "1992", title = "Analysis of a {QR} Algorithm for Computing Singular Values", institution = "Yale University", address = "New Haven, CT", type = "{Tech. Report}", number = "YALEU/DCS/RR-917", kwds = "svd, ord", } @article{chip:94a, author = "S. Chandrasekaran and I. C. F. Ipsen", year = "1994", title = "Backward Errors for Eigenvalue and Singular Value Decompositions", journal = "Numer. Math.", volume = "68", pages = "215--223", kwds = "svd, pert", } @article{chip:94, author = "S. Chandrasekaran and I. C. F. Ipsen", year = "1994", title = "On Rank-Revealing Factorizations", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "592--622", kwds = "qrd, rank, rrqrd" } @article{chpa:96, author = "X.-W. Chang and C. C. Paige", year = "1996", title = "A New Perturbation Analysis for the {Cholesky} Factorization", journal = "IMA J. Numer. Anal.", notes = "submitted", volume = "", pages = "", kwds = "chol, pert" } @article{chvv:88, author = "J. Charlier and M. Vanbegin and P. {Van Dooren}", year = "1988", title = "On Efficient Implementations of {Kogbetliantz's} Algorithm for Computing the Singular Value Decomposition", journal = "Numer. Math.", volume = "52", pages = "279--300", kwds = "svd, prll " } @article{chhe:93, author = "S. Chatterjee and G. Heller", year = "1993", title = "The Numerical Effect of Measurement Error in the Explanatory Variables on the Observed Least Squares Estimate", journal = "SIAM J. Matrix Anal. Appl.", volume = "14", pages = "677--687", kwds = "err, regr" } @techreport{chen:75, author = "Y. T. Chen", year = "1975", title = "Iterative Methods for Linear Least Squares Problems", institution = "University of Waterloo, Canada", type = "{Tech. Report}", number = "CS-75-04", note = "", kwds = "iter" } @article{chte:72, author = "Y. T. Chen and R. P. Tewarson", year = "1972", title = "On the Fill-in when Sparse Vectors are Orthonormalized", journal = "Computing", volume = "9", pages = "53--56", kwds = "sparse, orth" } @phdthesis{chu:88, author = "E. C. H. Chu", year = "1988", title = "Orthogonal Decomposition of Dense and Sparse Matrices on Multiprocessors", school = "University of Waterloo", address = "Canada", type = "{Ph. D.} thesis", kwds = "qrd, prll" } @article{chge:89, author = "E. C. H. Chu and J. A. George", year = "1989", title = "{QR} Factorization of a Dense Matrix on a Hypercube Multiprocessor", journal = "Parallel Comput.", volume = "11", pages = "55--71", kwds = "qrd, prll" } @techreport{chgl:84, author = "E. C. H. Chu and J. A. George and J. Liu and E. Ng", year = "1984", title = "{SPARSPAK}: Waterloo Sparse Matrix Package User's Guide for {SPARSPAK-A}", institution = "Department of Computer Science, University of Waterloo", address = "Canada", type = "Res. Report", number = "CS-84-36", note = "", kwds = "sparse, soft" } @article{chkl:87, author = "J. Chun and T. Kailath and H. Lev-Ari", year = "1987", title = "Fast Parallel Algorithms for {QR} and Triangular Factorizations", journal = "SIAM J. Sci. Statist. Comput.", volume = "8", pages = "899--913", kwds = "qrd, toep" } ci- @article{cimm:39, author = "G. Cimmino", year = "1939", title = "Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari", journal = "Ric. Sci. Progr. Tecn. Econom. Naz.", volume = "9", pages = "326--333", kwds = "iter, prll" } cl- @article{clos:86, author = "D. I. Clark and M. R. Osborne", year = "1986", title = "Finite Algorithms for {Hubers's} {M}-Estimator", journal = "SIAM J. Sci. Statist. Comput.", volume = "7", pages = "72--85", kwds = "err" } @article{clos:88, author = "D. I. Clark and M. R. Osborne", year = "1988", title = "On Linear Restricted and Interval Least-squares Problems", journal = "IMA J. Numer. Anal.", volume = "8", pages = "23--36", kwds = "err" } @article{clin:73, author = "A. K. Cline", year = "1973", title = "An Elimination Method for the Solution of Linear Least squares problems", journal = "SIAM J. Numer. Anal.", volume = "10", pages = "283--289", kwds = "lud, ne" } @techreport{clin:75, author = "A. K. Cline", year = "1975", title = "The Transformation of a Quadratic Programming Problem into Solvable Form", institution = "NASA, Langley Research Center, Hampton, VA.", type = "{Tech. Report}", number = "ICASE 75-14", note = "", kwds = "quadpr" } @incollection{clcv:82, author = "A. K. Cline and A. R. Conn and C. F. {Van Loan}", year = "1982", title = "Generalizing the {LINPACK} Condition Estimator", editor = "J. P. Hennart", booktitle = "Numerical Analysis", publisher = "Springer-Verlag, Berlin", series = "Lecture Notes in Mathematics", volume = "909", kwds = "cond, err" } @article{clms:79, author = "A. K. Cline and C. B. Moler and G. W. Stewart and J. H. Wilkinson", year = "1979", title = "An Estimate for the Condition Number of a Matrix", journal = "SIAM J. Numer. Anal.", volume = "16", pages = "368--375", kwds = "cond, err" } @article{clpl:76, author = "R. E. Cline and R. J. Plemmons", year = "1976", title = "$\ell_2$-solutions to Underdetermined Linear Systems", journal = "SIAM Review", volume = "18", pages = "92--106", kwds = "uds" } co- @incollection{cool:90, author = "J. W. Cooley", year = "1990", title = "How the {FFT} Gained Acceptance", editor = "S. G. Nash", booktitle = "A History of Scientific Computing", publisher = "Addison-Wesley, Reading, MA", pages = "133--140", kwds = "fft" } @article{cotu:65, author = "J. W. Cooley and J. W. Tukey", year = "1965", title = "An Algorithm for the Machine Calculation of Complex {Fourier} Series", journal = "Math. Comp.", volume = "19", pages = "297--301", kwds = "fft" } @article{colw:69, author = "J. W. Cooley and P. A. W. Lewis and P. D. Welsh", year = "1969", title = "The Fast {Fourier} Transform and its Application", journal = "IEEE Trans. Education", volume = "E-12", pages = "27--34", kwds = "fft" } @article{coeg:86, author = "T. F. Coleman and A. Edenbrandt and J. R. Gilbert", year = "1986", title = "Predicting Fill for Sparse Orthogonal Factorization", journal = "J. Assoc. Comput. Mach.", volume = "33", pages = "517--532", kwds = "sparse, fill" } @article{cohu:89, author = "T. F. Coleman and L. A. Hulbert", year = "1989", title = "A Direct Active Set Algorithm for Large Sparse Quadratic Programs with Simple Lower Bounds", journal = "Math. Programming", volume = "45", pages = "373--406", kwds = "sparse, constr" } @article{cohu:93, author = "T. F. Coleman and L. A. Hulbert", year = "1993", title = "A Globally and Superlinearly Convergent Algorithm for Convex Quadratic Programs with Simple Bounds", journal = "SIAM J. Optim.", volume = "3", pages = "298--321", kwds = "sparse, constr" } @article{coli:92, author = "T. F. Coleman and Y. Li", year = "1992", title = "A Global and Quadratically Convergent Affine Scaling Method for Linear $l_1$ Problems", journal = "Math. Programming", volume = "56", pages = "189--222", kwds = "rob" } @article{coli:92a, author = "T. F. Coleman and Y. Li", year = "1992", title = "A Global and Quadratically Convergent Affine Scaling Method for Linear $l_\infty$ Problems", journal = "SIAM J. Numer. Anal.", volume = "29", pages = "1166--1186", kwds = "cheb" } @techreport{coli:93, author = "T. F. Coleman and Y. Li", year = "1993", title = "An Interior {Newton} Method for Quadratic Programming", institution = "Department of Computer Science, Cornell University", address = "Ithaca, NY", type = "{Tech. Report}", number = "TR 93-1388", kwds = "constr" } @article{cott:74, author = "R. W. Cottle", year = "1974", title = "Manifestations of the {Schur} Complement", journal = "Linear Algebra Appl.", volume = "8", pages = "189--211", kwds = "nla, augms" } @inproceedings{cott:77, author = "R. W. Cottle", year = "1977", title = "Numerical Methods for Complementarity Problems in Engineering and Applied Science", pages = "37--52", editor = "R. Glowinski and J. L. Lions", booktitle = "Computing Methods in Applied Sciences and Engineering", publisher = "Springer-Verlag, New York", series = "Lecture Notes in Mathematics", volume = "704", kwds = "constr, iter" } @article{cogs:78, author = "R. W. Cottle and G. H. Golub and R. S. Sacher", year = "1978", title = "On the Solution of Large Structured Linear Complementarity Problems: The Block Partitioned Case", journal = "Appl. Math. Optim.", volume = "4", pages = "347--363", kwds = "nla, augms" } @article{cox:81, author = "M. G. Cox", year = "1981", title = "The Least Squares Solution of Overdetermined Linear Equations having Band or Augmented Band Structure", journal = "IMA J. Numer. Anal.", volume = "1", pages = "3--22", kwds = "sparse, band" } @incollection{cox:90, author = "M. G. Cox", year = "1990", title = "The Least-squares Solution of Linear Equations with Block-angular Observation Matrix", pages = "227--240", booktitle = "Reliable Numerical Computation", editor = "M. G. Cox and S. J. Hammarling", publisher = "Oxford University Press, UK", kwds = "sparse, basys" } @article{crai:55, author = "E.~J. Craig", year = "1955", title = "The $N$-step Iteration Procedure", journal = "J. Math. Phys.", volume = "34", pages = "65--73", kwds = "iter, cg" } @techreport{crgh:80, author = "R. L. Crane and B. S. Garbow and K. E. Hillstrom and M. Minkoff", year = "1980", title = "{LCLSQ}: An Implementation of an Algorithm for Linearly Constrained Linear Least Squares", institution = "Argonne National Laboratory", address = " Argonne, IL", type = "{Tech. Report}", number = "ANL-80-116", kwds = "constr" } @article{crwa:79, author = "P. Craven and G. Wahba", year = "1979", title = "Smoothing Noisy Data with Spline Functions", journal = "Numer. Math.", volume = "31", pages = "377--403", kwds = "spline, regul" } @article{crye:71, author = "C. Cryer", year = "1971", title = "The Solution of a Quadratic Programming Problem using Systematic Overrelaxation", journal = " SIAM J. Control Optim.", volume = "9", pages = "385--392", kwds = "quadpr, iter" } @article{cuwl:83, author = "J. K. Cullum and R. A. Willoughby and M. Lake", year = "1983", title = "A {Lanczos} Algorithm for Computing Singular Values and Vectors of Large Matrices", journal = "SIAM J. Sci. Statist. Comput.", volume = "4", pages = "197--215", kwds = "svd, lanczos" } @book{cuwi:85, author = "J. K. Cullum and R. A. Willoughby", year = "1985", title = "{Lanczos} Algorithms for Large Symmetric Eigenvalue Computations", volume = "1 Theory. 2 Programs", publisher = "Birkh{\"a}user", address = "Stuttgart", kwds = "lanczos" } @inproceedings{cuth:72, author = "E. Cuthill", year = "1972", title = "Several Strategies for Reducing the Bandwidth of Matrices", pages = "157--166", editor = "D. J. Rose and R. A. Willoughby", booktitle = "Sparse Matrices and Their Applications", publisher = "Plenum Press, New York", kwds = "sparse, fill, band" } @article{cybe:84, author = "G. Cybenko", year = "1984", title = "The Numerical Stability of the Lattice Algorithm for Least Squares Linear Prediction Problems", journal = "BIT", volume = "24", pages = "441--455", kwds = "err, toep" } @article{cybe:87, author = "G. Cybenko", year = "1987", title = "Fast {Toeplitz} Orthogonalization Using Inner Products", journal = "SIAM J. Sci. Statist. Comput.", volume = "8", pages = "734--740", kwds = "qrd, toep" } da- @article{dass:68, author = "G. Dahlquist and B. Sj{\"o}berg and P. Svensson", year = "1968", title = "Comparison of the Method of Averages with the Method of Least Squares", journal = "Math. Comp.", volume = "22", pages = "833--846", kwds = "appr" } @article{dgks:76, author = "J. Daniel and W. B. Gragg and L. Kaufman and G. W. Stewart", year = "1976", title = "Reorthogonalization and Stable Algorithms for Updating the {Gram-Schmidt} {QR} Factorization", journal = "Math. Comp.", volume = "30", pages = "772--95", kwds = "qrd, orth, upd, downd" } @book{dawo:80, author = "C. Daniel and F. S. Wood", year = "1980", title = "Fitting Equations to Data, {\rm 2nd ed.}", publisher = "John Wiley", address = "New York", kwds = "stat, regr" } @article{daka:70, author = "C. Davis and W. Kahan", year = "1970", title = "The Rotation of Eigenvectors by a Perturbation {III}", journal = "SIAM J. Numer. Anal.", volume = "7", pages = "1--46", kwds = "eig, csd" } @article{daxa:89, author = "A. Dax", year = "1989", title = "The $\ell_1$ Solution of Linear Equations Subject to Linear Constraints", journal = "SIAM J. Sci. Statist. Comput.", volume = "10", pages = "328--340", kwds = "rob, constr" } @article{daxa:93, author = "A. Dax", year = "1993", title = "On Row Relaxation Methods for Large Constrained Least Squares Problems", journal = "SIAM J. Sci. Comput.", volume = "14", pages = "570--584", kwds = "iter, constr" } de- @article{deba:79, author = "L. M. Delves and I. Barrodale", year = "1979", title = "A Fast Direct Method for the Least Squares Solution of Slightly Overdetermined Sets of Linear Equations", journal = "J. Inst. Maths. Applic.", volume = "24", pages = "149--156", kwds = "lud" } @article{deme:89, author = "C.~J. Demeure", year = "1989", title = "Fast {QR} Factorization of {Vandermonde} Matrices", journal = "Linear Algebra Appl.", volume = "122/3/4", pages = "165--194", kwds = "vand" } @article{deme:90, author = "C.~J. Demeure", year = "1990", title = "{QR} Factorization of Confluent {Vandermonde} Matrices", journal = "IEEE Trans. Acoust. Speech Signal Process.", volume = "38 (10)", pages = "1799--1802", kwds = "vand" } @article{demm:87, author = "J. Demmel", year = "1987", title = "The Smallest Perturbation of a Submatrix which Lowers the Rank and Constrained Total Least Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "24", pages = "199-206", kwds = "max, tls, constr, rank" } @article{dehi:93, author = "J. Demmel and N. J. Higham", year = "1993", title = "Improved Error Bounds for Underdetermined System Solvers", journal = "SIAM J. Matrix Anal. Appl.", volume = "14", pages = "1--14", kwds ="uds, err" } @article{deka:90, author = "J. Demmel and W. Kahan", year = "1990", title = "Accurate Singular Values of Bidiagonal Matrices", journal = "SIAM J. Sci. Statist. Comput.", volume = "11", pages = "873--912", kwds = "svd, err" } @article{demo:93, author = "B. {De Moor}", year = "1993", title = "Structured Total Least Squares and $L_2$ Approximation Problems", journal = "Linear Algebra Appl.", volume = "188/189", pages = "163--206", kwds = "tls, sigp" } @article{demo:94, author = "B. {De Moor}", year = "1994", title = "On the Structure of Generalized Singular Value and {QR} Decompositions", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "347--358", kwds = "qr, gsvd" } @techreport{dego:89, author = "B. {De Moor} and G. H. Golub", year = "1989", title = "Generalized Singular Value Decomposition: A Proposal for a Standard Nomenclature", institution = "Numerical Analysis Project", address = "Stanford University, CA", type = "{Tech. Report}", number = "NA-89-05", kwds = "gsvd, glsq, tls, sigp" } @article{dego:91, author = "B. {De Moor} and G. H. Golub", year = "1991", title = "The Restricted Singular Value Decomposition: Properties and Applications", journal = "SIAM J. Matrix. Anal. Appl.", volume = "12", pages = "401--425", kwds = "gsvd, glsq, tls, sigp" } @article{devd:92, author = "B. {De Moor} and P. {Van Dooren}", year = "1992", title = "Generalizations of the Singular Value and {QR} Decompositions", journal = "SIAM J. Matrix. Anal. Appl.", volume = "13", pages = "993--1014", kwds = "gsvd, gqrd" } @inproceedings{denn:77, author = "J. E. Dennis", year = "1977", title = "Nonlinear Least Squares and Equations", pages = "269--312", booktitle = "The State of the Art in Numerical Analysis", editor = "D. A. H. Jacobs", publisher = "Academic Press, New York", kwds = "nlsq, survey" } @article{degw:81, author = "J. E. Dennis and D. M. Gay and R. E. Welsch", year = "1981", title = "An Adaptive Nonlinear Least-squares Algorithm", journal = "ACM Trans. Math. Software", volume = "7", pages = "348--368", kwds = "nlsq" } @article{degw:81a, author = "J. E. Dennis and D. M. Gay and R. E. Welsch", year = "1981", title = "Algorithm {\rm 573} {NL{\rm 2}SOL}: An Adaptive Nonlinear Least-squares Algorithm", journal = "ACM Trans. Math. Software", volume = "7", pages = "369--383", kwds = "nlsq, soft" } @article{degw:83, author = "J. E. Dennis and D. M. Gay and R. E. Welsch", year = "1983", title = "Remark on Algorithm {\rm 573}", journal = "ACM Trans. Math. Software", volume = "9", pages = "139", kwds = "nlsq, soft" } @book{desc:83, author = "J. E. Dennis and R. B. Schnabel", year = "1983", title = "Numerical Methods for Unconstrained Optimization and Nonlinear Equations", publisher = "Prentice Hall", address = "Englewood Cliffs, NJ", kwds = "nlsq, opt" } @article{dest:86, author = "J. E. Dennis and T. Steihaug", year = "1986", title = "On the Successive Projection Approach to Least Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "23", pages = "717--733", kwds = "iter, sparse, prll" } @inproceedings{deap:78, author = "P. Deuflhard and V. Apostolescu", year = "1978", title = "An Underrelaxed {Gauss--Newton} Method for Equality Constrained Nonlinear Least Squares", booktitle = "Proceedings 8th IFIP Conference on Optimization Techniques", editor = "J. Stoer", publisher = "Springer-Verlag, Berlin", series = "Lecture Notes in Control and Information Science", volume = "7", pages = "22--32", kwds = "nlsq, constr" } @inproceedings{deap:80, author = "P. Deuflhard and V. Apostolescu", year = "1980", title = "A Study of the {Gauss--Newton} Algorithm for the Solution of Nonlinear Least Squares Problems", booktitle = "Special Topics of Applied Mathematics", editor = "J. Frehse and D. Pallaschke and U. Trottenberg", publisher = "North-Holland, Amsterdam", kwds = "nlsq" } @article{desa:80, author = "P. Deuflhard and W. Sautter", year = "1980", title = "On Rank-Deficient Pseudoinverses", journal = "Linear Algebra Appl.", volume = "29", pages = "91--111", kwds = "rank,ginv" } @book{dobm:79, author = "J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart", year = "1979", title = "LINPACK Users' Guide", publisher = "SIAM", address = "Philadelphia", kwds = "lud, cond, qrd, svd, upd, downd, soft, survey" } @article{dodd:90, author = "J. J. Dongarra and J. {Du Croz} and I. S. Duff and S. Hammarling", year = "1990", title = "A Set of Level {\rm 3} Basic Linear Algebra Subprograms", journal = "ACM Trans. Math. Software", volume = "16", pages = "1--17", kwds = "prll, blas, soft" } @article{ddhh:88, author = "J. J. Dongarra and J. {Du Croz} and S. Hammarling and R. J. Hanson", year = "1988", title = "An Extended Set of {Fortran} Basic Linear Algebra Subprograms", journal = "ACM Trans. Math. Software", volume = "14", pages = "1--17", kwds = "blas, prll, soft" } @article{dogr:87, author = "J. J. Dongarra and E. Grosse", year = "1987", title = "Distribution of Mathematical Software via Electronic Mail", journal = "Comm. ACM", volume = "30", pages = "403--407", kwds = "soft" } @article{drma:96, author = "Z. Drma\v{c}", year = "1997", title = "Implementation of {Jacobi} Rotations for Accurate Singular Value Computation in Floating Point Arithmetic", journal = "SIAM J. Sci. Comput.", note = "to appear", volume = "18", pages = "", kwds = "svd" } @book{drsm:81, author = "N. R. Draper and H. Smith", year = "1981", title = "Applied Regression Analysis, {\rm 2nd ed.}", publisher = "John Wiley", address = "New York", kwds = "stat, regr" } @article{duff:74, author = "I. S. Duff", year = "1974", title = "Pivot Selection and Row Orderings in {Givens} Reduction on Sparse Matrices", journal = "Computing", volume = "13", pages = "239--248", kwds = "perm, sparse, fill" } @article{duff:77, author = "I. S. Duff", year = "1977", title = "A Survey of Sparse Matrix Research", journal = "Proceedings of the IEEE", volume = "65", pages = "500--535", kwds = "survey, sparse" } @article{duff:77a, author = "I. S. Duff", year = "1977", title = "On Permutations to Block Triangular Form", journal = "J. Inst. Maths. Applic.", volume = "19", pages = "339--342", kwds = "survey, sparse" } @article{duff:81, author = "I. S. Duff", year = "1981", title = "On Algorithms for Obtaining a Maximum Transversal", journal = "ACM Trans. Math. Software", volume = "7", pages = "315--330", kwds = "perm, sparse" } @article{duff:86, author = "I. S. Duff", year = "1986", title = "Parallel Implementation of Multifrontal Schemes", journal = "Parallel Computing", volume = "3", pages = "193--204", kwds = "prll, sparse" } @inproceedings{duff:94, author = "I. S. Duff", year = "1994", title = "The Solution of Augmented Systems", pages = "", booktitle = "Numerical Analysis 1993: Proceedings of the 15th Dundee Conference, June 1993", editor = "D. F. Griffiths and G. A. Watson", publisher = "Longman Scientific and Technical, Harlow, UK", series = "Pitman Research Notes in Mathematics", kwds = "sparse, aug, soft" } @book{duer:86, author = "I. S. Duff and A. M. Erisman and J. K. Reid", year = "1986", title = "Direct Methods for Sparse Matrices", publisher = "Oxford University Press", address = "London", kwds = "sparse, survey" } @article{dume:89, author = "I. S. Duff and G. A. Meurant", year = "1989", title = "The Effect of Ordering on Preconditioned Conjugate Gradients", journal = "BIT", volume = "29", pages = "635--657", kwds = "sparse, precond " } @article{dugr:91, author = "I. S. Duff and N. I. M. Gould and J. K. Reid and J. A. Scott and K. Turner", year = "1991", title = "The Factorization of Sparse Symmetric Indefinite Matrices", journal = "IMA J. Numer. Anal.", volume = "11", pages = "181--204", kwds = "sparse, augms " } @article{GouldScott:16, author = "N.I.M. Gould and J.A. Scott", year = "2016", title = "A Note on Performance Profiles for Benchmarking Software", journal = "Trans. Math. Softw.", volume = "43", number ="2", pages = "1--5", } @article{dugl:89, author = "I. S. Duff and R. G. Grimes and J. G. Lewis", year = "1989", title = "Sparse Matrix Test Problems", journal = "ACM Trans. Math. Software", volume = "15", pages = "1--14", kwds = "sparse, soft, test" } @techreport{dugl:92, author = "I.S. Duff and R.G. Grimes and J.G. Lewis", year = "1992", title = "User's Guide for {Harwell-Boeing} Sparse Matrix Test Problems Collection", institution = "Computing and Information Systems Department", address = "Rutherford Appleton Laboratory, Didcot, UK", type = "{Tech. Report}", number = "RAL-92-086", kwds = "sparse, soft, test" } @techreport{dumr:95, author = "I. S. Duff and M. Marrone and G. Radicati and C. Vittoli", year = "1995", title = "A Set of Level {\rm 3} Basic Linear Algebra Subprograms for Sparse Matrices", institution = "Computing and Information Systems Department", address = "Rutherford Appleton Laboratory, Didcot, UK", type = "{Tech. Report}", number = "RAL-TR-95-049", kwds = "soft" } @article{dumn:79, author = "I. S. Duff and N. Munksgaard and H. B. Nielsen and J. K. Reid", year = "1979", title = "Direct Solution of Sets of Linear Equations whose Matrix is Sparse Symmetric and Indefinite", journal = "J. Inst. Maths. Applic.", volume = "23", pages = "235--250", kwds = "sparse, augms" } @article{dure:76, author = "I. S. Duff and J. K. Reid", year = "1976", title = "A Comparison of Some Methods for the Solution of Sparse Overdetermined Systems of Linear Equations", journal = "J. Inst. Maths. Applic.", volume = "17", pages = "267--280", kwds = "sparse, survey" } @article{dure:78, author = "I. S. Duff and J. K. Reid", year = "1978", title = "An Implementation of {Tarjan's} Algorithm for the Block Triangularization of a Matrix", journal = "ACM Trans. Math. Software", volume = "4", pages = "137--147", kwds = "sparse, graph" } @article{dure:79, author = "I. S. Duff and J. K. Reid", year = "1979", title = "Some Design Features of a Sparse Matrix Code", journal = "ACM Trans. Math. Software", volume = "5", pages = "18--35", kwds = "sparse,lud" } @techreport{dure:82, author = "I. S. Duff and J. K. Reid", year = "1982", title = "{MA{\rm 27}}---{A} Set of {Fortran} Subroutines for Solving Sparse Symmetric Sets of Linear Equations", institution = "AERE, Harwell", address = "Oxfordshire, UK", type = "{Tech. Report}", number = "R.10533", kwds = "sparse, soft" } @article{dure:83, author = "I. S. Duff and J. K. Reid", year = "1983", title = "The Multifrontal Solution of Indefinite Sparse Symmetric Linear Systems", journal = "ACM Trans. Math. Software", volume = "9", pages = "302--325", kwds = "sparse,multfr " } @techreport{dure:95, author = "I. S. Duff and J. K. Reid", year = "1995", title = "{MA{\rm 47}}, {A Fortran} Code for Direct Solution of Indefinite Sparse Symmetric Linear Systems", institution = "Rutherford Appleton Laboratory", address = "Didcot, UK", type = "{Tech. Report}", number = "RAL-95-001", kwds = "sparse, soft" } @book{dust:78, editor = "I. S. Duff and G. W. Stewart", year = "1978", title = "Sparse Matrix Proceedings", publisher = "SIAM", address = "Philadelphia", kwds = "sparse, survey" } @article{dufo:64, author = "H. M. Dufour", year = "1964", title = "R{\'e}solution des Systemes Lin{\'e}aires par la M{\'e}thode des R{\'e}sidues Conjugu{\'e}s", journal = "Bull. G{\'e}od{\'e}sique", volume = "71", pages = "65--87", kwds = "sparse, cg " } @article{dume:58, author = "A.~L. Dulmage and N.~S. Mendelsohn", year = "1958", title = "Coverings of Bipartite Graphs", journal = "Canad. J. Math.", volume = "10", pages = "517--534", kwds = "sparse, graph " } @article{dume:59, author = "A.~L. Dulmage and N.~S. Mendelsohn", year = "1959", title = "A Structure Theory of Bipartite Graphs of Finite Exterior Dimension", journal = "Trans. Roy. Soc. Canada", volume = "53, III", pages = "1--13", kwds = "sparse, graph " } @article{dume:63, author = "A.~L. Dulmage and N.~S. Mendelsohn", year = "1963", title = "Two Algorithms for Bipartite Graphs", journal = "J. Soc. Indust. Appl. Math.", volume = "11", pages = "183--194", kwds = "sparse, graph " } @article{dwye:44, author = "P. S. Dwyer", year = "1944", title = "A Matrix Presentation of Least Squares and Correlation Theory with Matrix Justification of Improved Methods of Solution", journal = "Ann. Math. Statist.", volume = "15", pages = "82-89", kwds = "stat, regr" } @article{dwye:45, author = "P. S. Dwyer", year = "1945", title = "The Square Root Method and its Use in Correlation and Regression", journal = " J. Amer. Statist. Assoc.", volume = "40", pages = "493--503", kwds = "chol, regr" } @book{dwye:51, author = "P. S. Dwyer", year = "1951", title = "Linear Computations", publisher = "John Wiley", address = "New York", kwds = "stat, regr, survey" } @article{ecyo:36, author = "C. Eckart and G. Young", year = "1936", title = "The Approximation of One Matrix by Another of Lower Rank", journal = "Psychometrica", volume = "1", number = "3", pages = "211--218", kwds = "max, rank" } @techreport{eila:75, author = "E. L. Eichhorn and C. L. Lawson", year = "1975", title = "An {ALGOL} Procedure for Solution of Constrained Least Squares Problems", institution = "JPL", address = "Pasadena, CA", type = "Computing Memorandum", number = "No. 374", kwds = "constr, soft" } @article{eiss:81, author = "S. C. Eisenstat and M. H. Schultz and A. H. Sherman", year = "1981", title = "Algorithms and Data Structures for Sparse Symmetric {Gaussian} Elimination", journal = "SIAM J. Sci. Statist. Comput.", volume = "2", pages = "225--237", kwds = "sparse, soft, ne" } @article{eigs:82, author = "S. C. Eisenstat and M. C. Gurky and M. H. Schultz and A. H. Sherman", year = "1982", title = "Yale Sparse Matrix Package, {\rm 1:} {The} Symmetric Codes.", journal = "Internat. J. Numer. Methods Engrg.", volume = "18", pages = "235--250", kwds = "sparse, soft, ne" } @techreport{eiip:93, author = "S. C. Eisenstat and I.~C.~F. Ipsen", year = "1993", title = "Relative Perturbation Techniques for Singular Value Problems", institution = "Yale University", address = "New Haven, CT", type = "{Tech. Report}", number = "YALEU/DCS/RR-942", kwds = "svd, pert", } @article{ekbl:88, author = "H. Ekblom", year = "1988", title = "A New Algorithm for the {Huber} Estimator in Linear Models", journal = "BIT", volume = "28", pages = "60--76", kwds = "rob, regr" } @article{elde:77, author = "L. ELD\'EN", year = "1977", title = "Algorithms for the Regularization of Ill-conditioned Least Squares Problems", journal = "BIT", volume = "17", pages = "134--145", kwds = "regul, illp" } @article{elde:80, author = "L. Eld\'en", year = "1980", title = "Perturbation Theory for the Least Squares Problem with Linear Equality Constraints", journal = "SIAM J. Numer. Anal.", volume = "17", pages = "338--350", kwds = "pert, constr" } @article{elde:83, author = "L. Eld\'en", year = "1983", title = "A Weighted Pseudoinverse, Generalized Singular Values, and Constrained Least Squares Problems", journal = "BIT", volume = "22", pages = "487--502", kwds = "ginv, constr, wlsq" } @article{elde:84, author = "L. Eld\'en", year = "1984", title = "An Efficient Algorithm for the Regularization of Ill-conditioned Least Squares Problems with a Triangular {Toeplitz} Matrix", journal = "SIAM J. Sci. Statist. Comput.", volume = "5", pages = "229--236", kwds = "regul, illp, toep" } @article{elde:84a, author = "L. Eld\'en", year = "1984", title = "An Algorithm for the Regularization of Ill-conditioned Banded Least Squares Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "5", pages = "237--254", kwds = "regul, illp" } @article{elde:84c, author = "L. Eld\'en", year = "1984", title = "A Note on the Computation of the Generalized Cross-validation Function for Ill-conditioned Least Squares Problems", journal = "BIT", volume = "24", pages = "467--472", kwds = "regul, illp" } @techreport{elde:88, author = "L. Eld\'en", year = "1988", title = "Parallel {QR} Decomposition of a Rectangular Matrix", institution = "Link{\"o}ping University", address = "Sweden", type = "{Tech. Report}", number = "LiTH-MAT-R-78-3", kwds = "qrd, prll" } @article{elpa:94, author = "L. Eld\'en and H. Park", year = "1994", title = "Block Downdating of Least Squares Solutions", journal = "SIAM J. Matrix. Anal. Appl.", volume = "15", pages = "1018--1034", kwds = "upd, block" } @article{elpa:94a, author = "L. Eld\'en and H. Park", year = "1994", title = "Perturbation Analysis for Block Downdating of a {Cholesky} Decomposition", journal = "Numer. Math.", volume = "68", pages = "457--467", kwds = "downd, block" } @article{elsc:86, author = "L. Eld\'en and R. Schreiber", year = "1986", title = "A Systolic Array for the Regularization of Ill-Conditioned Least-Squares Problems with Triangular {Toeplitz} Matrix", journal = "Linear Algebra Appl.", volume = "77", pages = "137-147", kwds = "prll, toep, regul" } @techreport{elsk:82, author = "L. Eld\'en and I. Skoglund", year = "1982", title = "Algorithms for the Regularization of Ill-Conditioned Least Squares Problems with Tensor Product Structure, and Application to Space-Invariant Image Restoration", institution = "Link{\"o}ping University", address = "Sweden", type = "{Tech. Report}", number = "LiTH-MAT-R-82-48", kwds = "kron, regul" } @techreport{elfv:78, author = "T. Elfving", year = "1978", title = "On the Conjugate Gradient Method for Solving Linear Least Squares Problems", institution = "Link{\"o}ping University", address = "Sweden", type = "{Tech. Report}", number = "LiTH-MAT-R-78-3", kwds = "cg, iter" } @article{elfv:80, author = "T. Elfving", year = "1980", title = "Block-iterative Methods for Consistent and Inconsistent Linear Equations", journal = "Numer. Math.", volume = "35", pages = "1--12", kwds = "iter, uds, prll" } @article{erti:75, author = "A. M. Erisman and W. F. Tinney", year = "1975", title = "On Computing Certain Elements of the Inverse of a Sparse Matrix", journal = "Comm. ACM", volume = "18", pages = "177--179", kwds = "covar, sparse" } @article{evli:88, author = "D. J. Evans and C. Li", year = "1988", title = "{Gauss--Seidel} and {SOR} Methods for Least Squares Problems", journal = "Numer. Math.", volume = "53", pages = "485--498", kwds = "iter" } @article{evli:89, author = "D. J. Evans and C. Li", year = "1989", title = "Numerical Aspects of the Generalized cg-Method Applied to Least Squares Problems", journal = "Computing", volume = "41", pages = "171--178", kwds = "cg, iter" } @article{evli:90, author = "D. J. Evans and C. Li", year = "1990", title = "The Theoretical Aspects of the GCG-Method Applied to Least-Squares Problems", journal = " Internat. J. Comput. Math.", volume = "35", pages = "207--229", kwds = "cg, iter" } %fa- @article{fakf:68, author = "D. K. Faddeev and V. N. Kublanovskaya and V. N. Faddeeva", year = "1968", title = "Solution of Linear Algebraic Systems with Rectangular Matrices", journal = "Proc. Steklov Inst. Math.", volume = "96", pages = "", kwds = "rank, qrd" } @incollection{fakf:68a, author = "D. K. Faddeev and V. N. Kublanovskaya and V. N. Faddeeva", year = "1968", title = "Sur les syst{\`e}mes lin{\'e}aires alg{\'e}briques de matrices rectangularies et malcondition{\'e}es", pages = "161--170", booktitle = "Programmation en Math{\'e}matiques Num{\'e}riques", publisher = "Editions Centre Nat. Recherche Sci., Paris VII", kwds = "qrd, rank" } @article{faho:55, author = "K. Fan and A.J. Hoffman", year = "1955", title = "Some Metric Inequalities in the Space of Matrices", journal = "Proc. Amer. Math. Soc.", volume = "6", pages = "111--116", kwds = "max" } @inproceedings{fare:85, author = "R. W. Farebrother", year = "1985", title = "The Statistical Estimation of the Standard Linear Model, {\rm 1756--1853}", pages = "77--99", booktitle = "Proc. First Internat. Tampere Seminar on Linear Statistical Models Appl. 1983", editor = "T. Pukkila and S. Puntanen", address = "University of Tampere, Tampere, Finland", kwds = "stat, hist" } @book{fare:88, author = "R. W. Farebrother", year = "1988", title = "Linear Least Squares Computations", publisher = "Marcel Dekker", address = "New York", kwds = "hist, survey" } @article{fafu:94, author = "D. W. Fausett and C. T. Fulton", year = "1994", title = "Large Least Squares Problems Involving {Kronecker} Products", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "219--227", kwds = "kron,qr" } @article{fern:89, author = "K. V. Fernando", year = "1989", title = "Linear Convergence of the Row Cyclic {Jacobi} and {Kogbetliantz} Methods", journal = "Numer. Math.", volume = "56", pages = "73--91", kwds = "svd" } @article{fepa:94, author = "K. V. Fernando and B. N. Parlett", year = "1994", title = "Accurate Singular Values and Differential qd Algorithms", journal = "Numer. Math.", volume = "67", pages = "191-229", kwds = "svd" } @techreport{fier:94, author = "R. D. Fierro", year = "1994", title = "Perturbation Analysis For Two-Sided (or Complete) Orthogonal Decompositions", institution = "Department of Mathematics, California State University", address = "San Marcos, CA", type = "{Tech. Report}", number = "PAM 94-02", kwds = "rrqrd, pert" } @article{fibu:94b, author = "R. D. Fierro and J. R. Bunch", year = "1994", title = "Collinearity and Total Least Squares", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "1167--1181", kwds = "tls" } @article{fibu:95, author = "R. D. Fierro and J. R. Bunch", year = "1995", title = "Orthogonal Projection and Total Least Squares", journal = "Numer. Linear Algebra Appl.", volume = "2", pages = "135--154", kwds = "tls" } @article{fibu:96, author = "R. D. Fierro and J. R. Bunch", year = "1996", title = "Perturbation Theory for Orthogonal Projection Methods With Applications to Least Squares and Total Least Squares", journal = "Linear Algebra Appl.", volume = "234", pages = "71--96", kwds = "pert,tls" } %fl- @article{flet:68, author = "R. Fletcher", year = "1968", title = "Generalized Inverse Methods for the Best Least Squares Solution of Systems of Non-Linear Equations", journal = "Comput. J.", volume = "10", pages = "392--399", kwds = "ginv, nlsq" } @article{flet:76, author = "R. Fletcher", year = "1976", title = "Factorizing Symmetric Indefinite Matrices", journal = "Linear Algebra Appl.", volume = "14", pages = "257--272", kwds = "augms" } @article{flet:85, author = "R. Fletcher", year = "1985", title = "Expected Conditioning", journal = "IMA J. Numer. Anal.", volume = "5", pages = "247--273", kwds = "cond, err" } @book{flet:87, author = "R. Fletcher", year = "1987", title = "Practical Methods of Optimization, {\rm 2nd ed.}", publisher = "John Wiley", address = "New York", kwds = "nlsq, opt, survey" } @article{flxu:87, author = "R. Fletcher and C. Xu", year = "1987", title = "Hybrid Methods for Nonlinear Least Squares", journal = "IMA J. Numer. Anal.", volume = "7", pages = "371--389", kwds = "cond, err" } @techreport{forb:89a, author = "A. B. Forbes", year = "1989", title = "Least-Squares Best-Fit Geometric Elements", institution = "National Physical Laboratory", address = "Teddington, UK", type = "{Tech. Report}", number = "NPL DITC 140/89", note = "", kwds = "nlsq" } @techreport{forb:89b, author = "A. B. Forbes", year = "1989", title = "Robust Circle and Sphere Fitting by Least Squares", institution = "National Physical Laboratory", address = "Teddington, UK", type = "{Tech. Report}", number = "NPL DITC 153/89", note = "", kwds = "nlsq" } @incollection{forb:90, author = "A. B. Forbes", year = "1990", title = "Least Squares Best Fit Geometrical Elements", pages = "311--319", booktitle = "Algorithms for Approximation II", editor = "J. C. Mason and M. G. Cox", publisher = "Chapman \& Hall, London", kwds = "nlsq" } @article{fors:56, author = "G. E. Forsythe", year = "1956", title = "Generation and Use of Orthogonal Polynomials for Data-fitting with a Digital Computer", journal = "J. Soc. Indust. Appl. Math.", volume = "5", pages = "74--88", kwds = "poly" } @article{fogo:65, author = "G. E. Forsythe and G. H. Golub", year = "1965", title = "On the Stationary Values of a Second Degree Polynomial on the Unit Sphere", journal = "J. Soc. Indust. Appl. Math.", volume = "13", pages = "1050--1068", kwds = "upd" } @book{fomm:77, author = "G. E. Forsythe and M. A. Malcolm and C. B. Moler", year = "1977", title = "Computer Methods for Mathematical Computations", publisher = "Prentice-Hall", address = "Englewood Cliffs, NJ", kwds = "survey, la, soft" } @book{fomo:67, author = "G. E. Forsythe and C. B. Moler", year = "1967", title = "Computer Solution of Linear Algebraic Systems", publisher = "Prentice-Hall", address = "Englewood Cliffs, NJ", kwds = "survey, la" } @article{fost:86, author = "L. V. Foster", year = "1986", title = "Rank and Nullspace Calculations Using Matrix Decompositions Without Column Interchanges", journal = "Linear Algebra Appl.", volume = "74", pages = "47--71", kwds = "rank, rrqrd, qrd" } @article{fost:90, author = "L. V. Foster", year = "1990", title = "The Probability of Large Diagonal Elements in the {QR} Factorization", journal = "SIAM J. Sci. Statist. Comput.", volume = "11", pages = "531--544", kwds = "rank, qrd" } @inproceedings{fost:91, author = "L. V. Foster", year = "1991", title = "Modifications of the Normal Equations Method that are Numerically Stable", pages = "501--512", booktitle = "Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms", editor = "G. H. Golub and P. {Van Dooren}", series = "NATO ASI Series", publisher = "Springer-Verlag, Berlin", kwds = "ne, grsch, ir, err" } @techreport{fome:92, author = "R. Fourer and S. Mehrotra", year = "1992", title = "Solving Symmetric Indefinite Systems in an Interior Point Method for Linear Programming", institution = "Department of Industrial Engineering and Management Science", address = "Northwestern University, Evanston, IL", type = "{Tech. Report}", number = "92-01", kwds = "augm, sparse, intpoint" } @techreport{fral:88, author = "C. Fraley", year = "1988", title = "Algorithms for Nonlinear Least Squares", institution = "Center for Large Scale Scientific Computation, Stanford University", address = "CA", number = "STAN-CLaSSiC-88-22", note = "", kwds = "nlsq, survey" } @article{fral:89, author = "C. Fraley", year = "1989", title = "Computational Behavior of {Gauss--Newton} Methods", journal = "SIAM J. Sci. Statist. Comput.", volume = "10", pages = "515--532", kwds = "nlsq" } @article{freu:87, author = "R. Freund", year = "1987", title = "A Note on Two Block {SOR} Methods for Sparse Least Squares Problems", journal = "Linear Algebra Appl.", volume = "88/89", pages = "211--221", kwds = "iter" } @article{frgn:91, author = "R.~W. Freund and G.~H. Golub and N. Nachtigal", year = "1991", title = "Iterative Solution of Linear Systems", journal = "Acta Numerica", volume = "1", pages = "57--100", kwds = "iter" } ga- @techreport{gand:80, author = "W. Gander", year = "1980", title = "Algorithms for the {QR}-decomposition", institution = "Angewandte Mathematik, ETH", address = "Z{\"u}rich, Switzerland", type = "{Tech. Report}", number = "80--02", note = "", kwds = "qrd, grsch" } @article{gand:81, author = "W. Gander", year = "1981", title = "Least Squares with a Quadratic Constraint", journal = "Numer. Math.", volume = "36", pages = "291-307", kwds = "constr, regul" } @article{gags:94, author = "W. Gander and G. H. Golub and R. Strebel", year = "1994", title = "Least-Squares Fitting of Circles and Ellipses", journal = "BIT", volume = "34", pages = "558--578", kwds = "nlsq" } @incollection{gama:93, author = "W. Gander and U. von Matt", year = "1993", title = "Some Least Squares Problems", pages = "69--87", booktitle = "Solving Problems in Scientific Computing Using {Maple} and {\sc MATLAB}", editor = "W. Gander and J. H\v{r}bi\v{c}ek ", publisher = "Springer-Verlag, Berlin", kwds = "nlsq" } @techreport{garz:51, author = "A. de la Garza", year = "1951", title = "An Iterative Method for Solving Systems Linear Equations", institution = "Union Carbide", address = "Oak Ridge, TN", type = "{Tech. Report}", number = "K-731", kwds = "iter, prll" } @book{gaus:1809, author = "C. F. Gauss", year = "1963", title = "Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, {\rm C. H. Davis, Trans.}", publisher = "Dover", address = "New York", note = "First published in 1809", kwds = "stat, nlsq, regr, ne" } @incollection{gaus:1810, author = "C. F. Gauss", year = "1880", title = "Disquisitio de Elementis Ellipticis {Palladis}", booktitle = "Werke, {\rm VI}", publisher = "K{\"o}niglichen Gesellschaft der Wissenschaften zu G{\"o}ttingen", pages = "1--24", note = "First published in 1810", kwds = "stat, nlsq, regr, ne" } @incollection{gaus:1821, author = "C. F. Gauss", year = "1880", title = "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae, Pars Prior", booktitle = "Werke, IV", publisher = "K{\"o}niglichen Gesellschaft der Wissenschaften zu G{\"o}ttingen", pages = "1--26", note = "First published in 1821", kwds = "regr, ne" } @incollection{gaus:1823, author = "C. F. Gauss", year = "1880", title = "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae, Pars Posterior", booktitle = "Werke, IV", publisher = " K{\"o}niglichen Gesellschaft der Wissenschaften zu G{\"o}ttingen", pages = "27-53", note = "First published in 1823", kwds = "regr, ne, upd" } @incollection{gaus:1826, author = "C. F. Gauss", year = "1880", title = "Theoria Combinationis Observationum Erroribus Minimis Obnoxiae, Supplementum", booktitle = "Werke, IV", publisher = "K{\"o}niglichen Gesellschaft der Wissenschaften zu G{\"o}ttingen", pages = "55--93", note = "First published in 1826", kwds = "stat, geod, iter" } @book{gaus:95, author = "C. F. Gauss", year = "1995", title = "Theory of the Combination of Observations Least Subject to Errors. Part {\rm 1}, Part {\rm 2}, Supplement, {\rm G. W. Stewart, Trans.}", publisher = "SIAM", address = "Philadelphia", kwds = "stat, ne, upd" } @article{gay:83, author = "D. M. Gay", year = "1983", title = "Algorithm {\rm 611}. {Subroutines} for Unconstrained Minimization Using a Model/Trust-region Approach", journal = " ACM Trans. Math. Software", volume = "9", pages = "503--524", kwds = "nlsq, soft" } @inproceedings{gay:84, author = "D. M. Gay", year = "1984", title = "A Trust-region Approach to Linearly Constrained Optimization", pages = "72--105", booktitle = "Proceedings of the 1983 Dundee Conference on Numerical Analysis", editor = "D.F. Griffiths", publisher = "Springer-Verlag, Berlin", series = " Lecture Notes in Mathematics", volume = "1066", kwds = "nlsq" } @inproceedings{gay:88, author = "D. M. Gay", year = "1988", title = "Interval Least Squares---a Diagnostic Tool", pages = "183--206", booktitle = "Reliability in Computing", editor = "R. E. Moore", publisher = "Academic Press, London", kwds = "err" } ge- @article{gent:73, author = "W. M. Gentleman", year = "1973", title = "Least Squares Computations by {Givens} Transformations Without Square Roots", journal = "J. Inst. Maths. Applic.", volume = "12", pages = "329--336", kwds = "qrd, rot" } @article{gent:75, author = "W. M. Gentleman", year = "1975", title = "Error Analysis of {QR} Decompositions by {Givens} Transformations", journal = "Linear Algebra Appl.", volume = "10", pages = "189--197", kwds = "err, rot" } @inproceedings{gent:76, author = "W. M. Gentleman", year = "1976", title = "Row Elimination for Solving Sparse Linear Systems and Least Squares Problems", booktitle = "Proceedings of the Dundee Conference on Numerical Analysis 1975", editor = "G. A. Watson", publisher = "Springer-Verlag, Berlin", series = " Lecture Notes in Mathematics", volume = "506", pages = "122--133", kwds = "sparse, perm" } @phdthesis{geor:71, author = "J. A. George", year = "1971", title = "Computer Implementation of the Finite-Element Method", school = "Stanford University, CA", type = "{Ph. D.} thesis", kwds = "sparse" } @article{gehe:80, author = "J. A. George and M. T. Heath", year = "1980", title = "Solution of Sparse Linear Least Squares Problems Using {Givens} Rotations", journal = "Linear Algebra Appl.", volume = "34", pages = "69--83", kwds = "sparse, qrd, rot" } @article{gehp:81, author = "J. A. George and M. T. Heath and R. J. Plemmons", year = "1981", title = "Solution of Large-Scale Sparse Least Squares Problems Using Auxiliary Storage", journal = "SIAM J. Sci. Statist. Comput.", volume = "2", pages = "416--429", kwds = "sparse, qrd" } @article{gehn:83, author = "J. A. George and M. T. Heath and E. G. Ng", year = "1983", title = "A Comparison of Some Methods for Solving Sparse Linear Least Squares Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "4", pages = "177--187", kwds = "sparse, test" } @book{geli:81, author = "J. A. George and J. W.-H. Liu", year = "1981", title = "Computer Solution of Large Sparse Positive Definite Systems", publisher = "Prentice-Hall", address = "Englewood Cliffs, NJ", kwds = "sparse, survey" } @article{geli:87, author = "J. A. George and J. W.-H. Liu", year = "1987", title = "{Householder} Reflections versus {Givens} Rotations in Sparse Orthogonal Decomposition", journal = "Linear Algebra Appl.", volume = "88/89", pages = "223--238", kwds = "sparse, rot, qrd" } @article{geli:89, author = "J. A. George and J. W.-H. Liu", year = "1989", title = "The Evolution of the Minimum Degree Ordering Algorithm", journal = "SIAM Review", volume = "31", pages = "1--19", kwds = "sparse, perm, hist" } @article{geln:84, author = "J. A. George and J. W.-H. Liu and E. G. Ng", year = "1984", title = "Row Ordering Schemes for Sparse {Givens} Transformations, {I.} {Bipartite} Graph Model", journal = "Linear Algebra Appl.", volume = "61", pages = "55--81", kwds = "sparse, perm, rot" } @article{geln:86, author = "J. A. George and J. W.-H. Liu and E. G. Ng", year = "1986", title = "Row Ordering Schemes for Sparse {Givens} Transformations, {II.} {Implicit} Graph Model", journal = "Linear Algebra Appl.", volume = "75", pages = "203--223", kwds = "sparse, perm, rot" } @article{geln:86a, author = "J. A. George and J. W.-H. Liu and E. G. Ng", year = "1984", title = "Row Ordering Schemes for Sparse {Givens} Transformations, {III.} {Analysis} for a Model Problem", journal = "Linear Algebra Appl.", volume = "75", pages = "225--240", kwds = "sparse, perm, rot" } @article{geng:83, author = "J. A. George and E. G. Ng", year = "1983", title = "On Row and Column Orderings for Sparse Least Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "20", pages = "326--344", kwds = "sparse, perm, rot" } @techreport{geng:84, author = "J. A. George and E. G. Ng", year = "1984", title = "{SPARSPAK}: Waterloo Sparse Matrix Package User's Guide for {SPARSPAK-B}", institution = "Department of Computer Science, University of Waterloo", address = "Canada", type = "Res. Report", number = "CS-84-37", note = "", kwds = "sparse, soft" } @article{geng:85, author = "J. A. George and E. G. Ng", year = "1985", title = "An Implementation of {Gaussian} Elimination with Partial Pivoting for Sparse Systems", journal = "SIAM J. Sci. Statist. Comput.", volume = "6", pages = "390--409", kwds = "sparse, lud" } @article{geng:87, author = "J. A. George and E. G. Ng", year = "1987", title = "Symbolic Factorization for Sparse {Gaussian} Elimination with Partial Pivoting", journal = "SIAM J. Sci. Statist. Comput.", volume = "8", pages = "877--898", kwds = "sparse, lud" } @article{geng:88, author = "J. A. George and E. G. Ng", year = "1988", title = "On the Complexity of Sparse {QR and LU} Factorization of Finite-Element Matrices", journal = "SIAM J. Sci. Statist. Comput.", volume = "9", pages = "849--861", kwds = "sparse, qrd, lud" } @article{geln:88, author = "J. A. George and J. W.-H. Liu and E. G. Ng", year = "1988", title = "A Data Structure for Sparse {QR and LU} Factorization", journal = "SIAM J. Sci. Statist. Comput.", volume = "9", pages = "100--121", kwds = "sparse, qrd, lud" } @article{gepv:78, author = "J. A. George and W. G. Poole and R. G. Voigt", year = "1978", title = "Incomplete Nested Dissection for Solving $n$ by $n$ Grid Problems", journal = "SIAM J. Numer. Anal.", volume = "15", pages = "90--112", kwds = "sparse, perm, nestdis" } gi- @phdthesis{gilb:80, author = "J. R. Gilbert", year = "1980", title = "Graph Separator Theorems and Sparse {Gaussian} Elimination", school = "Stanford University, CA", type = "{Ph. D.} thesis", kwds = "sparse, graph" } @article{gilb:94, author = "J. R. Gilbert", year = "1994", title = "Predicting Structure in Sparse Matrix Computation", journal = "SIAM J. Matrix. Anal. Appl.", volume = "15", pages ="62--79", kwds = "sparse, soft" } @article{gims:92, author = "J. R. Gilbert and C. Moler and R. Schreiber", year = "1992", title = "Sparse Matrices in {MATLAB}: Design and Implementation", journal = "SIAM J. Matrix. Anal. Appl.", volume = "13", pages ="333--356", kwds = "sparse, soft" } @techreport{ginp:93, author = "J. R. Gilbert and E. G. Ng and B. W. Peyton", year = "1993", title = "Separators and Structure Prediction in Sparse Orthogonal Factorization", institution = "Xerox Corporation, Palo Alto Research Center", type = "{Tech. Report}", number = "CSL-93-15", kwds = "sparse, qrd" } @article{gipe:88, author = "J. R. Gilbert and T. Peierls", year = "1988", title = "Sparse Partial Pivoting in Time Proportional to Arithmetic Operations", journal = "SIAM J. Sci. Statist. Comput.", volume = "9", pages ="862--874", kwds = "sparse" } @article{ggms:74, author = "P. E. Gill and G. H. Golub and W. Murray and M.A. Saunders", year = "1974", title = "Methods for Modifying Matrix Factorizations", journal = "Math. Comp", volume = "28", pages = "505--535", kwds = "upd, downd, chol, qrd" } @techreport{gihm:86, author = "P. E. Gill and S. J. Hammarling and W. Murray and M. A. Saunders and M. H. Wright", year = "1986", title = "User's Guide for {LSSOL} (version {\rm 1.0}): a {Fortran} Package for Constrained Linear Least-squares and Convex Quadratic Programming", institution = "Department of Operations Research, Stanford University", type = "{Report SOL}", address = "CA", kwds = "constr, quadpr, soft" } @inproceedings{gimu:76, author = "P. E. Gill and W. Murray", year = "1976", title = "Nonlinear Least Squares and Nonlinearly Constrained Optimization", booktitle = "Proceedings Dundee Conference on Numerical Analysis 1975", editor = "G. A. Watson", publisher = "Springer-Verlag, Berlin", series = " Lecture Notes in Mathematics", volume = "506", pages = "135--147", kwds = "nlsq, quadpr" } @inproceedings{gimu:76a, author = "P. E. Gill and W. Murray", year = "1976", title = "The Orthogonal Factorization of a Large Sparse Matrix", pages = "201--212", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = "Academic Press, New York", kwds = "sparse, qrd" } @article{gimu:78, author = "P. E. Gill and W. Murray", year = "1978", title = "Algorithms for the Solution of the Nonlinear Least Squares Problem", journal = "SIAM J. Numer. Anal.", volume = "15", pages = "977--992", kwds = "nlsq" } @book{gimw:81, author = "P. E. Gill and W. Murray and M. H. Wright", year = "1981", title = "Practical Optimization", publisher = "Academic Press", address = "London and New York", kwds = "nlsq, opt, survey" } @inproceedings{gmsw:90, author = "P. E. Gill and W. Murray and M. A. Saunders and M. H. Wright", year = "1990", title = "A {Schur}-complement Method for Sparse Quadratic Programming", booktitle = "Reliable Numerical Computation", editor = "M. G. Cox and S. Hammarling", pages = "113--138", publisher = "Clarendon Press, Oxford, UK", kwds = "sparse, quadpr, augms" } @article{give:58, author = "W. Givens", year = "1958", title = "Computation of Plane Unitary Rotations Transforming a General Matrix to Triangular Form", journal = " SIAM J. Appl. Math.", volume = "6", pages = "26--50", kwds = "qrd, rot" } @article{glsm:90, author = "J. Gluchowska and A. Smoktunowicz", year = "1990", title = "Solving the Linear Least Squares Problem with Very High Relative Accuracy", journal = "Computing", volume = "45", pages = "345--354", kwds = "err, ir" } @book{gold:77, author = "H.~H. Goldstine", year = "1977", title = "A History of Numerical Analysis from the {\rm 16}th through the {\rm 19}th Century", publisher = "Springer-Verlag", address = "New York", kwds = "hist" } @article{golu:65, author = "G. H. Golub", year = "1965", title = "Numerical Methods for Solving Least Squares Problems", journal = "Numer. Math.", volume = "7", pages = "206-216", kwds = "qrd, upd" } @article{golu:68, author = "G. H. Golub", year = "1968", title = "Least Squares, Singular Values and Matrix Approximations", journal = "Aplikace Matematiky", volume = "13", pages = "44--51", kwds = "svd, max" } @inproceedings{golu:69, author = "G. H. Golub", year = "1969", title = "Matrix Decompositions and Statistical Computation", pages = "365--397", booktitle = "Statistical Computation", editor = "R.C. Milton and J. A. Nelder", publisher = "Academic Press, New York", kwds = "qrd, grsch, stat" } @article{golu:73, author = "G. H. Golub", year = "1973", title = "Some Modified Matrix Eigenvalue Problems", journal = "SIAM Review", volume = "15", pages = "318--344", kwds = "upd" } @article{gohw:79, author = "G. H. Golub and M. T. Heath and G. Wahba", year = "1979", title = "Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter", journal = "Technometrics", volume = "21", pages = "215--223", kwds = "regul" } @article{gohs:87, author = "G. H. Golub and A. Hoffman and G.W. Stewart", year = "1987", title = "A Generalization of the {Eckart-Young-Mirsky} Matrix Approximation Theorem", journal = "Linear Algebra Appl.", volume = "88/89", pages = "317--327", kwds = "max" } @article{goka:65, author = "G. H. Golub and W. Kahan", year = "1965", title = "Calculating the Singular Values and Pseudo-inverse of a Matrix", journal = "SIAM J. Numer. Anal. Ser. B", volume = "2", pages = "205--224", kwds = "svd, lanczos" } @techreport{goks:76, author = "G. H. Golub and V. Klema and G. W. Stewart", year = "1976", title = "Rank Degeneracy and Least Squares Problems", institution = "Computer Science Department, Stanford University", address = "CA", type = " {Tech. Report}", number = "STAN-CS-76-559, August 1976", kwds = "rank, rrqrd" } @inproceedings{golv:79, author = "G. H. Golub and R. J. LeVeque", year = "1979", title = "Extensions and Uses of the Variable Projection Algorithm for Solving Nonlinear Least Squares Problems", pages = "1--12", booktitle = "Proceedings of the 1979 Army Numerical Analysis and Computers Conf. ", publisher = "White Sands Missile Range, White Sands, NM, ARO Report 79-3", kwds = "nlsq, varpro" } @inproceedings{golu:77, author = "G. H. Golub and F. T. Luk", year = "1977", title = "Singular Value Decomposition: Applications and Computations", booktitle = "Trans. 22nd Conference of Army Mathematicians, ARO Report 77-1", pages = "577--605", kwds = "svd" } @article{golo:81, author = "G. H. Golub and F. T. Luk and M. L. Overton", year = "1981", title = "A Block {Lanczos} Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix", journal = "ACM Trans. Math. Software", volume = "7", pages = "149--169", kwds = "svd, lanczos" } @inproceedings{golp:79, author = "G. H. Golub and F. T. Luk and M. Pagano", year = "1979", title = "A Sparse Least Squares Problem in Photogrammetry", booktitle = "Proceedings of the Computer Science and Statistics 12th Annual Symposium on the Interface", editor = "J. F. Gentleman", publisher = "University of Waterloo, Canada", pages = "26--30", kwds = "sparse, nestdis" } @article{gomt:86, author = "G. H. Golub and P. Manneback and P. Toint", year = "1986", title = "A Comparison Between some Direct and Iterative Methods for Large Scale Geodetic Least Squares Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "7", pages = "799--816", kwds = "sparse, nestdis, iter, cg, precond" } @inproceedings{gosv:95, author = "G. H. Golub and K. Solna and P. {Van Dooren}", year = "1995", title = "A {QR}-Like {SVD} Algorithm for a Product/Quotient of Several Matrices", booktitle = "{SVD} and Signal Processing, III: Algorithms, Architectures and Applications", editor = "M. Moonen and B. {De Moor}", pages = "139--147", publisher = "Elsevier Science B.V., Amsterdam", kwds = "gqrd, gsvd" } @article{goma:91, author = "G. H. Golub and U. von Matt", year = "1991", title = "Quadratically Constrained Least Squares and Quadratic Problems", journal = "Numer. Math.", volume = "59", pages = "561--580", kwds = "regul, constr", } @article{gona:82, author = "G. H. Golub and S. G. Nash", year = "1982", title = " Nonorthogonal Analysis of Variance using a Generalized Conjugate-Gradient Algorithm", journal = "J. Amer. Statist. Assoc.", volume = "77", pages = "109--116", kwds = "cg, stat", } @article{gopedupl:73, author = "G. H. GOLUB and V. PEREYRA", year = "1973", title = "The Differentiation of Pseudoinverses and Nonlinear Least Squares Problems Whose Variables Separate", journal = "SIAM J. Numer. Anal.", volume = "10", pages = "413--432", kwds = "pert, ginv, varpro," } @inproceedings{gope:76, author = "G. H. Golub and V. Pereyra", year = "1976", title = "Differentiation of Pseudoinverses, Separable Nonlinear Least Squares Problems and Other Tales", booktitle = "Generalized Inverses and Applications", editor = "M. Z. Nashed", pages = "303--324", publisher = "Academic Press, New York", kwds = "pert, ginv, varpro," } @article{gopl:80, author = "G. H. Golub and R. J. Plemmons", year = "1980", title = "Large-Scale Geodetic Least-Squares Adjustment by Dissection and Orthogonal Decomposition", journal = "Linear Algebra Appl.", volume = "34", pages = "3--28", kwds = "sparse, qrd, geod, nestdis" } @inproceedings{gops:88, author = "G. H. Golub and R. J. Plemmons and A. Sameh", year = "1988", title = "Parallel Block Schemes for Large-Scale Least-Squares Computations", pages = "171-179", booktitle = "High-Speed Computing, Scientific Applications and Algorithm Design", publisher = "University of Illinois Press", address = "", kwds = "iter, prll" } @article{gore:70, author = "G. H. Golub and C. Reinsch", year = "1970", title = "Singular Value Decomposition and Least Squares Solution", journal = "Numer. Math.", volume = "14", pages = "403--420", kwds = "svd, rank, reg" } @inproceedings{gosa:70, author = "G. H. Golub and M. A. Saunders", year = "1970", title = "Linear Least Squares and Quadratic Programming", pages = "229--256", booktitle = "Integer and Nonlinear Programming", editor = "J. Abadie", publisher = "North-Holland, Amsterdam", kwds = "qrd, opt, quadpr" } @article{gost:73, author = "G. H. Golub and G. P. Styan", year = "1973", title = "Numerical Computations for Univariate Linear Models", journal = "J. Statist. Comput. Simul.", volume = "2", pages = "253-274", kwds = "stat, regr, qrd" } @techreport{goun:69, author = "G. H. Golub and R. Underwood", year = "1969", title = "Stationary Values of the Ratio of Quadratic Forms Subject to Linear Constraints", institution = "Computer Science Department, Stanford University, CA", type = "{Tech. Report}", number = "CS-142", note = "", kwds = "geig, regul" } @inproceedings{govl:79, author = "G. H. Golub and C. F. {Van Loan}", year = "1979", title = "Total least squares", pages = "69--76", booktitle = "Smoothing Techniques for Curve Estimation", editor = "T. Gasser and M. Rosenblatt", publisher = "Springer-Verlag, New York", kwds = "svd, tls" } @article{govl:80, author = "G. H. Golub and C. F. {Van Loan}", year = "1980", title = "An Analysis of the Total Least Squares Problem", journal = "SIAM J. Numer. Anal.", volume = "17", pages = "883-893", kwds = "svd, tls" } @book{govl:89, author = "G. H. Golub and C. F. {Van Loan}", year = "1989", title = "Matrix Computations, {\rm 2nd ed.}", publisher = "Johns Hopkins University Press", address = "Baltimore", kwds = "la, survey" } @article{gova:61, author = "G. H. Golub and R. S. Varga", year = "1961", title = "{Chebyshev} semi-iterative methods, successive Overrelaxation Iterative Methods and Second Order {Richardson} Iterative Methods, {Parts I and II}", journal = "Numer. Math.", volume = "3", pages = "147--168", kwds = "iter" } @inproceedings{gowi:65, author = "G. H. Golub and J. H. Wilkinson", year = "1965", title = "Iterative Refinement of Least Squares Solutions", booktitle = "Proceedings of the IFIP Congress 65, New York, 1965", editor = "W. A. Kalenich", pages = "606--607", publisher = "Spartan Books, Washington", kwds = "ir, qrd, err" } @article{gowi:66, author = "G. H. Golub and J. H. Wilkinson", year = "1966", title = "Note on the Iterative Refinement of Least Squares Solution", journal = "Numer. Math.", volume = "9", pages = "139-148", kwds = "ir, qrd, err" } @article{gozh:94, author = "G. H. Golub and H. Zha", year = "1994", title = "Perturbation Analysis of the Canonical Correlation of Matrix Pairs", journal = "Linear Algebra Appl.", volume = "210", pages = "3--28", kwds = "pert, err" } gr- @article{grha:84, author = "W. H. Gragg and W. J. Harrod", year = "1984", title = "The Numerically Stable Reconstruction of {Jacobi} Matrices from Spectral Data", journal = "Numer. Math.", volume = "44", pages = "317--335", kwds = "eigv" } @article{gram:1883, author = "J. P. Gram", year = "1883", title = "{\"U}ber die {E}ntwickelung reeller {F}unktionen in {R}eihen mittelst der {M}ethode der kleinsten {Q}uadrate", journal = "J. Reine Angew. Math.", volume = "94", pages = "41--73", kwds = "grsch" } @article{gree:89, author = "A. Greenbaum", year = "1989", title = "Behavior of Slightly Perturbed {Lanczos} and Conjugate-gradient Recurrences", journal = "Linear Algebra Appl.", volume = "113", pages = "7--63", kwds = "cg, lanczos" } @article{grst:92, author = "A. Greenbaum and Z. Strakos", year = "1992", title = "Predicting the Behavior of Finite Precision {Lanczos} and Conjugate Gradient Computations", journal = "SIAM J. Matrix Anal. Appl.", volume = "13", pages = "121-137", kwds = "cg, lanczos" } @article{grev:66, author = "T. E. Greville", year = "1966", title = "Note on the Generalized Inverse of a Matrix Product", journal = "SIAM Review", volume = "8", pages = "518--521", kwds = "ginv" } @book{grhi:85, author = "P. Griffiths and I. D. Hill", year = "1985", title = "Applied Statistical Algorithms", publisher = "Ellis Horwood Ltd.", address = "Chichester, UK", kwds = "stat" } @article{grle:81, author = "R.G. Grimes and J.G. Lewis", year = "1981", title = "Condition Number Estimation for Sparse Matrices", journal = "SIAM J. Sci. Statist. Comput.", volume = "2", pages = "384--388", kwds = "cond, sparse" } @article{gros:80, author = "E. Grosse", year = "1980", title = "Tensor Spline Approximations", journal = "Linear Algebra Appl.", volume = "34", pages = "29--41", kwds = "sparse, kron" } @techreport{GuEisenstat:92, author = "M. Gu and S. C. Eisenstat", year = "1992", title = "A Divide-And-Conquer Algorithm for the Bidiagonal {SVD}", institution = "Department of Computer Science, Yale University", address = "New Haven, CT", type = "{Tech. Report}", number = "YALEU/DCS/RR-933", kwds = "svd, downd", } @techreport{guei:93b, author = "M. Gu and S. C. Eisenstat", year = "1993", title = "A Stable and Fast Algorithm for Updating the Singular Value Decomposition", institution = "Department of Computer Science, Yale University", address = "New Haven, CT", type = "{Tech. Report}", number = "YALEU/DCS/RR-966", kwds = "svd, downd", } @techreport{GuEisenstat:94, author = "M. Gu and S. C. Eisenstat", year = "1994", title = "An Efficient Algorithm for Computing a Strong Rank-Revealing {QR} Decomposition", institution = "Department of Computer Science, Yale University", address = "New Haven, CT", type = "{Tech. Report}", number = "YALEU/DCS/RR-967", kwds = "rrqrd", } @article{guei:95, author = "M. Gu and S. C. Eisenstat", year = "1995", title = "A Divide-and-Conquer Algorithm for the Bidiagonal {SVD}", journal = "SIAM J. Matrix. Anal. Appl.", volume = "16", pages = "79--92", kwds = "svd, prll", } @article{guei:95a, author = "M. Gu and S. C. Eisenstat", year = "1995", title = "Downdating the Singular Value Decomposition", journal = "SIAM J. Matrix. Anal. Appl.", volume = "16", pages = "793--810", kwds = "svd, downd", } @phdthesis{gull:93, author = "M. Gulliksson", year = "1993", title = "Algorithms for Overdetermined Systems of Equations", school = "Institute of Information Processing, University of Ume{\aa}", address = "Ume{\aa}, Sweden", type = "{Ph. D.} thesis", number = "UMINF 93-11", kwds = "qrd, wlsq,nlsq" } @article{gull:94, author = "M. Gulliksson", year = "1994", title = "Iterative Refinement for Constrained and Weighted Linear Least Squares", journal = "BIT", volume = "34", pages = "239--253", kwds = "err, ir, wlsq, qrd", } @article{gull:95, author = "M. Gulliksson", year = "1995", title = "Backward Error Analysis for the Constrained and Weighted Linear Least Squares Problem when Using the Weighted {QR} Decomposition", journal = "SIAM J. Matrix. Anal. Appl.", volume = "16", pages = "675--687", kwds = "err, wlsq, qrd", } @article{gull:95b, author = "M. Gulliksson", year = "1995", title = "On Modified {Gram-Schmidt} for Weighted and Constrained Linear Least Squares", journal = "BIT", volume = "35", pages = "458--473", kwds = "err, wlsq, grsch", } @article{guwe:92, author = "M. Gulliksson and P.-{\AA}. Wedin", year = "1992", title = "Modifying the {QR} Decomposition to Constrained and Weighted Linear Least Squares", journal = "SIAM J. Matrix. Anal. Appl.", volume = "13:4", pages = "1298--1313", kwds = "qrd, wlsq" } @techreport{guwe:93, author = "M. Gulliksson and P.-{\AA}. Wedin", year = "1993", title = "Numerical Aspects on Algorithms for Overdetermined Linear Systems in $l_p$ Norm", institution = "Institute of Information Processing, University of Ume{\aa}", address = "Ume{\aa}, Sweden", type = "{Tech. Report}", number = "UMINF--93-11", kwds = "nlsq, wlsq, constr", } @techreport{gusw:93, author = "M. Gulliksson and I. S{\"o}derquist and P.-{\AA}. Wedin", year = "1993", title = "Algorithms for Weighted and Constrained Nonlinear Least Squares Using the Modified {QR} Decomposition", institution = "Institute of Information Processing, University of Ume\aa", address = "Ume{\aa}, Sweden", type = "{Tech. Report}", number = "UMINF--93-05", kwds = "nlsq, wlsq, constr", } @inproceedings{gust:76, author = "F. G. Gustavson", year = "1976", title = "Finding the Block Lower Triangular Form of a Matrix", pages = "275--289", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = "Academic Press, New York", kwds = "sparse" } ha- @incollection{hach:74, author = "G. D. Hachtel", year = "1974", title = "Extended Applications of the Sparse Tableau Approach---Finite Elements and Least Squares", booktitle = "Basic questions in design theory", editor = "W. Spillers", publisher = " North-Holland, Amsterdam", kwds = "sparse, augms" } @incollection{hach:76, author = "G. D. Hachtel", year = "1976", title = "The Sparse Tableau Approach to Finite Element Assembly", booktitle = "Sparse Matrix Computations", editor = "J.R. Bunch and D. J. Rose", publisher = "Academic Press, New York", kwds = "sparse, augms" } @article{haly:80, author = "L. A. Hageman and F. T. Luk and D. M. Young", year = "1980", title = "On the Equivalence of Certain Iterative Acceleration Methods", journal = "SIAM J. Numer. Anal.", volume = "17", pages = "852--873", kwds = "iter" } @book{hayo:81, author = "L. A. Hageman and D. M. Young", year = "1981", title = "Applied Iterative Methods", publisher = "Academic Press", address = "New York, London", kwds = "iter, survey" } @article{hage:84, author = "W. W. Hager", year = "1984", title = "Condition Estimates", journal = "SIAM J. Sci. Statist. Comput.", volume = "5", pages = "311--316", kwds = "cond, err" } @article{hage:89, author = "W. W. Hager", year = "1989", title = "Updating the Inverse of a Matrix", journal = "SIAM Review", volume = "31", pages = "221--239", kwds = "upd" } @article{hamm:74, author = "S. Hammarling", year = "1974", title = "A Note on Modifications to the {Givens} Plane Rotation", journal = "J. Inst. Maths. Applic.", volume = "13", pages = "215--218", kwds = "rot" } @techreport{hamm:85, author = "S. Hammarling", year = "1985", title = "The Numerical Solution of the General {Gauss-Markov} Linear Model", institution = "Numerical Algorithms Group Ltd.", address = "Oxford, UK", type = "NAG {Tech. Report}", number = "TR2/85", kwds = "glsq" } @inproceedings{hapy:90, author = "C. {-G}. Han and P. M. Pardalos and Y. Ye", year = "1990", title = "Computational Aspects of an Interior Point Algorithm for Quadratic Programming Problems with Box Constraints", booktitle = "Large Scale Numerical Optimization, Proceedings, Cornell University, Ithaca, October 19--20, 1989 ", editor = "T. F. Coleman and Y. Li", pages = "92--112", publisher = "SIAM, Philadelphia", kwds = "sparse, constr" } @article{hank:91, author = "M. Hanke", year = "1991", title = "Accelerated {Landweber} Iterations for the Solution of Ill-posed Equations", journal = "Numer. Math.", volume = "60", pages = "341--373", kwds = "illp, regul, iter" } @book{hank:95, author = "M. Hanke", year = "1995", title = "Conjugate Gradient Type Methods for Ill-posed Problems", publisher = "Longman Scientific and Technical, Harlow, UK", series = "Pitman Research Notes in Mathematics", kwds = "illp, regul, iter" } @article {MR2058859, AUTHOR = {Hanke, Martin}, TITLE = {On {L}anczos based methods for the regularization of discrete ill-posed problems}, NOTE = {BIT 40th Anniversary Meeting}, JOURNAL = {BIT}, FJOURNAL = {BIT. Numerical Mathematics}, VOLUME = {41}, YEAR = {2001}, NUMBER = {5, suppl.}, PAGES = {1008--1018}, ISSN = {0006-3835}, MRCLASS = {65F22}, MRNUMBER = {2 058 859}, } @article{haha:94, author = "M. Hanke and P. C. Hansen", year = "1994", title = "Regularization Methods for Large-Scale Problems", journal = "Surveys Math. Indust.", volume = "3", pages = "253--315", kwds = "illp, regul, sparse" } @article{hane:93, author = "M. Hanke and M. Neumann", year = "1992", title = "The Geometry of the Set of Scaled Projections", journal = "Linear Algebra Appl.", volume = "190", pages = "137--148", kwds = "wlsq" } @article{hans:87, author = "P. C. Hansen", year = "1987", title = "The Truncated {SVD} as a Method for Regularization", journal = "BIT", volume = "27", pages = "534--553", kwds = "svd, illp, regul" } @article{hans:90, author = "P. C. Hansen", year = "1990", title = "Truncated Singular Value Decomposition Solutions to Discrete Ill-Posed Problems with Ill-determined Numerical Rank", journal = "SIAM J. Sci. Statist. Comput.", volume = "11", pages = "503--518", kwds = "svd, illp, rank" } @article{hans:90a, author = "P. C. Hansen", year = "1990", title = "Relations between {SVD} and {GSVD} of Discrete Regularization Problems in Standard and General Form", journal = "Linear Algebra Appl.", volume = "141", pages = "165--176", kwds = "illp, regul,gsvd" } @article{hans:92, author = "P. C. Hansen", year = "1992", title = "Analysis of Ill-Posed Problems By Means of the {L}-Curve", journal = "SIAM Review", volume = "34", pages = "561--580", kwds = "illp, regul" } @phdthesis{hans:95, author = "P. C. Hansen", year = "1995", title = "Rank-Deficient and Discrete Ill-Posed Problems", school = "UNI$\bullet$C, Technical University of Denmark", address = "Lyngby, Denmark", type = "{Doctoral} thesis", number = "UNIC-95-07", kwds = "illp, regul" } @book {MR99a:65037, AUTHOR = {HANSEN, P.C.}, TITLE = {Rank-deficient and discrete ill-posed problems}, SERIES = {SIAM Monographs on Mathematical Modeling and Computation}, NOTE = {Numerical aspects of linear inversion}, PUBLISHER = {Society for Industrial and Applied Mathematics (SIAM)}, ADDRESS = {Philadelphia, PA}, YEAR = {1998}, PAGES = {xvi+247}, ISBN = {0-89871-403-6}, MRCLASS = {65F05 (65F10 65F20)}, MRNUMBER = {99a:65037}, MRREVIEWER = {Jin Xi Zhao}, } @article {MR94k:65062, AUTHOR = {HANSEN, P.C.}, TITLE = {Regularization tools: a {M}atlab package for analysis and solution of discrete ill-posed problems}, JOURNAL = {Numer. Algorithms}, FJOURNAL = {Numerical Algorithms}, VOLUME = {6}, YEAR = {1994}, NUMBER = {1-2}, PAGES = {1--35}, ISSN = {1017-1398}, MRCLASS = {65F30 (65F20)}, MRNUMBER = {94k:65062}, } @article {MR94h:65045, AUTHOR = {HANSEN, P.C. and O'LEARY, D.P.}, TITLE = {The use of the {$L$}-curve in the regularization of discrete ill-posed problems}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {14}, YEAR = {1993}, NUMBER = {6}, PAGES = {1487--1503}, ISSN = {1064-8275}, CODEN = {SJOCE3}, MRCLASS = {65F30 (65F20)}, MRNUMBER = {94h:65045}, MRREVIEWER = {Jose Cuminato}, } @article {MR93k:65035, AUTHOR = {HANSEN, P.C.}, TITLE = {Analysis of discrete ill-posed problems by means of the {${L}$}-curve}, JOURNAL = {SIAM Rev.}, FJOURNAL = {SIAM Review. A Publication of the Society for Industrial and Applied Mathematics}, VOLUME = {34}, YEAR = {1992}, NUMBER = {4}, PAGES = {561--580}, ISSN = {0036-1445}, CODEN = {SIREAD}, MRCLASS = {65F20 (65F30)}, MRNUMBER = {93k:65035}, MRREVIEWER = {Jin Xi Zhao}, } @article {MR91e:65058, AUTHOR = {HANSEN, P.C.}, TITLE = {Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank}, JOURNAL = {SIAM J. Sci. Statist. Comput.}, FJOURNAL = {Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing}, VOLUME = {11}, YEAR = {1990}, NUMBER = {3}, PAGES = {503--518}, ISSN = {0196-5204}, CODEN = {SIJCD4}, MRCLASS = {65F30}, MRNUMBER = {91e:65058}, MRREVIEWER = {Lars Eld{\'e}n}, } @article{hage:93, author = "P. C. Hansen and H. Gesmar", year = "1993", title = "Fast Orthogonal Decomposition of Rank Deficient Toeplitz Matrices", journal = "Numer. Algorithms", volume = "4", pages = "151-166", kwds = "qrd, toep" } @article{haol:93, author = "P. C. Hansen and D. O'Leary", year = "1993", title = "The Use of the {L}-Curve in the Regularization of Discrete Ill-Posed Problems", journal = " SIAM J. Sci. Comput.", volume = "14", pages = "1487--1503", kwds = "illp, regul" } @article{hans:86, author = "R. J. Hanson", year = "1986", title = "Linear Least Squares with Bounds and Linear Constraints", journal = " SIAM J. Sci. Statist. Comput.", volume = "7", pages = "826--834", kwds = "constr" } @article{hala:69, author = "R. J. Hanson and C. L. Lawson", year = "1969", title = "Extensions and Applications of the {Householder} Algorithm for Solving Linear Least Squares Problems", journal = "Math. Comp.", volume = "23", pages = "787--812", kwds = "nla, qrd, rank" } @article{haph:75, author = "R. J. Hanson and J. L. Phillips", year = "1975", title = "An Adaptive Numerical Method for Solving Linear {Fredholm} Equations of the First Kind", journal = "Numer. Math.", volume = "24", pages = "291--307", kwds = "regul" } @article{hjod:93, author = "D. R. G. Hare and C. R. Johnson and D. D. Olesky and P. V. D. Driessche", year = "1993", title = "Sparsity Analysis of the {QR} Factorization", journal = " SIAM J. Matrix. Anal. Appl.", volume = "14", pages = "655--669", kwds = "sparse" } @techreport{haha:79, author = "K. H. Haskell and R. J. Hanson", year = "1979", title = "Selected Algorithms for the Linearly Constrained Least Squares Problem: A User's Guide", institution = "Sandia National Laboratories, Albuquerque, NM", type = "{Tech. Report}", number = "SAND78-1290", note = "", kwds = "constr" } @article{haha:81, author = "K. H. Haskell and R. J. Hanson", year = "1981", title = "An Algorithm for Linear Least Squares Problems with Equality and Nonnegativity Constraints", journal = "Math Programming", volume = "21", pages = "98--118", kwds = "constr" } %he- @article{heat:82, author = "M. T. Heath", year = "1982", title = "Some extensions of an algorithm for sparse linear least squares problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "3", pages = "223--237", kwds = "sparse, qrd" } @article{heat:84, author = "M. T. Heath", year = "1984", title = "Numerical Methods for Large Sparse Linear Least Squares Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "5", pages = "497--513", kwds = "sparse, survey" } @article{help:86, author = "M. T. Heath and A. J. Laub and C. C. Paige and R. C. Ward", year = "1986", title = "Computing the {SVD} of a Product of Two Matrices", journal = "SIAM J. Sci. Statist. Comput.", volume = "7", pages = "1147--1149", kwds = "gsvd, jacobi" } @book{helm:80, author = "F. R. Helmert", year = "1880", title = "{Die Mathematischen und Physikalischen Theorien der h{\"o}heren Geod{\"a}sie, {\rm 1} Teil}", publisher = "Teubner", address = "Leipzig", kwds = "geod, nestdis" } @article{henr:79, author = "P. Henrici", year = "1979", title = "Fast {Fourier} Methods in Computational Complex Analysis", journal = "SIAM Review", volume = "21", pages = "481--527", kwds = "fft" } @article{hese:81, author = "H. V. Henderson and S. R. Searle", year = "1981", title = "The vec-Permutation Matrix, the vec operator and {Kronecker} Products: A Review", journal = "Linear and Multilinear Algebra", volume = "9", pages = "271--188", kwds = "kron" } @article{helr:73, author = "G. T. Herman and A. Lent and S. W. Rowland", year = "1973", title = "{ART}: {Mathematics} and Applications", journal = "J. Theoret. Biol.", volume = "42", pages = "1--32", kwds = "iter" } @article{hest:58, author = "M. R. Hestenes", year = "1958", title = "Inversion of Matrices by Biorthogonalization and Related Results", journal = "J. Soc. Indust. Appl. Math.", volume = "6", pages = "51--90", kwds = "cg, lanczos" } @article{hest:75, author = "M. R. Hestenes", year = "1975", title = "Pseudoinverses and Conjugate Gradients", journal = "Comm. ACM", volume = "18", pages = "40--43", kwds = "ginv, cg" } @article{hest:52, author = "M. R. Hestenes and E. Stiefel", year = "1952", title = "Methods of Conjugate Gradients for Solving Linear System", journal = "J. Res. Nat. Bur. Standards.", volume = "B49", pages = "409--436", kwds = "cg" } hi- @article{hieb:86, author = "K. L. Hiebert", year = "1986", title = "An Evaluation of Mathematical Software that Solves Nonlinear Least Squares Problems", journal = "ACM Trans. Math. Software", volume = "7", pages = "1--16", kwds = "nlsq, test" } @article{high:86, author = "N. J. Higham", year = "1986", title = "Computing the Polar Decomposition--with Applications", journal = "SIAM J. Sci. Statist. Comput.", volume = "7", pages = "1160--1174", kwds = "pold" } @article{high:87, author = "N. J. Higham", year = "1987", title = "A Survey of Condition Number Estimation for Triangular Matrices", journal = "SIAM Review", volume = "29", pages = "575-596", kwds = "nla, cond" } @article{high:87a, author = "N. J. Higham", year = "1987", title = "Error Analysis of the {Bj\"orck-Pereyra} Algorithms for Solving {Vandermonde} Systems", journal = "Numer. Math.", volume = "50", pages = "613--632", kwds = "err, vand" } @article{high:88, author = "N. J. Higham", year = "1988", title = "Computing a Nearest Symmetric Positive Semidefinite Matrix", journal = "Linear Algebra Appl.", volume = "103", pages = "103-118", kwds = "nla, max" } @article{high:88a, author = "N. J. Higham", year = "1988", title = "FORTRAN Codes for Estimating the One-norm of a Real or Complex Matrix, with Applications to Condition Estimation", journal = "ACM Trans. Math. Software", volume = "14", pages = "381--396", kwds = "cond, soft" } @article{high:88b, author = "N. J. Higham", year = "1988", title = "Fast Solution of {Vandermonde}-Like Systems Involving Orthogonal Polynomials", journal = "IMA J. Numer. Anal.", volume = "8", pages = "473--486", kwds = "vand" } @article{high:89, author = "N. J. Higham", year = "1989", title = "The Accuracy of Solutions to Triangular Systems", journal = "SIAM J. Numer. Anal.", volume = "26(5)", pages = "1252--1265", kwds = "err" } @inproceedings{high:90, author = "N. J. Higham", year = "1990", title = "Computing Error Bounds for Regression Problems", booktitle = "Contemporary Mathematics 112: Statistical Analysis of Measurement Error Models and Applications", editor = "P. J. Brown and W. A. Fuller", pages = "195--210", publisher = "American Mathematical Society, Providence, RI", kwds = "stat, nla, pert, regr" } @inproceedings{high:90b, author = "N. J. Higham", year = "1990", title = "Analysis of the {Cholesky} Decomposition of a Semi-definite Matrix", pages = "161--185", booktitle = "Reliable Numerical Computation", editor = "M. G. Cox and S. J. Hammarling", publisher = "Clarendon Press, Oxford", kwds = "chol" } @inproceedings{high:90c, author = "N. J. Higham", year = "1990", title = "How Accurate is {Gaussian} Elimination?", pages = "137--154", booktitle = "Numerical Analysis 1989: Proceedings of the 13th Dundee Conference", editor = "D. F. Griffiths and G. A. Watson", publisher = "Longman Scientific and Technical, Harlow, UK", series = "Pitman Research Notes in Mathematics 228", kwds = "nla, err" } @article{high:90d, author = "N. J. Higham", year = "1990", title = "Experience with a Matrix Norm Estimator", journal = "SIAM J. Sci. Statist. Comput.", volume = "11", pages = "804--809", kwds = "cond, err" } @article{high:91, author = "N. J. Higham", year = "1991", title = "Iterative Refinement Enhances the Stability of {QR} Factorization Methods for Solving Linear Equations", journal = "BIT", volume = "31", pages = "447-468", kwds = "qrd, ir" } @article{high:92, author = "N. J. Higham", year = "1992", title = "Estimating the matrix p-norm", journal = "Numer. Math.", volume = "62", pages = "539--556", kwds = "cond" } @inproceedings{high:94, author = "N. J. Higham", year = "1994", title = "A Survey of Componentwise Perturbation Theory in Numerical Linear Algebra", booktitle = "Mathematics of Computation 1943--1993. A Half Century of Computational Mathematics", series = "Proceedings of Symposia in Applied Mathematics", editor = "W. Gautschi", volume = "48", pages = "49--77", publisher = "American Mathematical Society, Providence, RI", kwds = "err" } @techreport{high:95, author = "N. J. Higham", year = "1995", title = "Stability of the Diagonal Pivoting Method with Partial Pivoting", institution = " Department of Mathematics, University of Manchester", address = "UK", type = "{Tech. Report}", number = "265, July 1995", kwds = "wlsq" } @book{high:95a, author = "N.J. HIGHAM", year = "1995", title = "Accuracy and Stability of Numerical Algorithms", publisher = "SIAM", address = "Philadelphia", kwds = "err, pert" } @inproceedings{hist:87, author = "N. J. Higham and G. W. Stewart", year = "1987", title = "Numerical Linear Algebra in Statistical Computing", booktitle = "The State of the Art in Numerical Analysis", editor = "A. Iserles and M. J. D. Powell", pages = "41--57", publisher = "Oxford University Press, London, UK", kwds = "la, stat" } ho- hu- @phdthesis{hoff:89a, author = "W. Hoffman", year = "1989", title = "Basic Transformations in Linear Algebra for Vector Computing", school = "University of Amsterdam", address = "the Netherlands", type = "{Ph. D.} thesis", kwds = "illp, regul" } @article{hoff:89, author = "W. Hoffman", year = "1989", title = "Iterative Algorithms for {Gram-Schmidt} Orthogonalization", journal = "Computing", volume = "41", pages = "335--348", kwds = "grsch, orth" } @article{hofl:79, author = "J. N. Holt and R. Fletcher", year = "1979", title = "An Algorithm for Constrained Non-linear Least-squares", journal = "J. Inst. Maths. Applic.", volume = "23", pages = "449--463", kwds = "nlsq, constr" } @article{hopa:92, author = "H. P. Hong and C. T. Pan", year = "1992", title = "Rank-Revealing {QR} factorization and {SVD}", journal = "Math. Comp.", volume = "58", pages = "213--232", kwds = "rrqrd" } @techreport{hova:94, author = "P. D. Hough and S. A. Vavasis", year = "1994", title = "Complete Orthogonal Decomposition for Weighted Least Squares", institution = "Advanced Computing Research Institute, Cornell University", address = "Ithaca, NY", type = "{Tech. Report}", number = "CTC93TR203, 12/94", kwds = "wlsq" } @article{hous:58, author = "A. S. Householder", year = "1958", title = "Unitary Triangularization of a Nonsymmetric Matrix", journal = "J. Assoc. Comput. Mach.", volume = "5", pages = "339--342", kwds = "nla, qrd" } @book{hous:74, author = "A. S. Householder", year = "1974", title = "The Theory of Matrices in Numerical Analysis", publisher = "Dover", address = "New York", kwds = "nla, survey" } @article{hoba:60, author = "A. S. Householder and F. L. Bauer", year = "1960", title = "On Certain Iterative Methods for Solving Linear Systems", journal = "Numer. Math.", volume = "2", pages = "55--59", kwds = "iter" } @book{hube:81, author = "P. J. Huber", year = "1981", title = "Robust Statistics", publisher = "John Wiley", address = "New York", kwds = "stat, rob" } @article{huho:85, author = "M. F. Hutchinson and F. R. de Hoog", year = "1985", title = "Smoothing Noisy Data with Spline Functions", journal = "Numer. Math.", volume = "47", pages = "99--106", kwds = "regul, spline" } @techreport{hwlp:93, author = "T.-M. Hwang and W.-W. Lin and D. L. Pierce", year = "1993", title = "An Alternate Column Selection Criterion for a Rank Revealing {QR} Factorization", institution = "Boeing Computer Services, Research and Technology", address = "Seattle, WA", type = "{Tech. Report}", number = "BCSTECH-93-021", kwds = "sparse, rrqrd" } @article{hwly:92, author = "T.-M. Hwang and W.-W Lin and E. K. Yang", year = "1992", title = "Rank Revealing {LU} Factorizations", journal = "Linear Algebra Appl.", volume = "175", pages = "115--141", kwds = "lud" } @incollection{ikra:85, author = "H. D. Ikramov", year = "1985", title = "Sparse Linear Least-Squares Problems", booktitle = "Advances in Sciences and Technology: Mathematical Analysis", volume = "23", editor = "R. V. Gamkredlidze", publisher = "Academy of Sciences, Moscow", note = "In Russian", pages = "219--285", kwds = "sparse, survey" } ja- je- jo- @article{jaco:45, author = "Jacobi, C. J. G.", year = "1845", title = "{{\"U}ber eine neue Aufl{\"o}sungsart der bei der Methode der kleinsten Quadrate vorkommenden line{\"a}ren Gleichungen}", journal = "Astronomische Nachrichten", volume = "22", number = "523", pages = "297--306", kwds = "qrd, rot" } @article{japh:91, author = "W. Jalby and B. Philippe", year = "1991", title = "Stability Analysis and Improvement of the Block {Gram-Schmidt} Algorithm", journal = "SIAM J. Sci. Statist. Comput.", volume = "12", pages = "1058--1073", kwds = "grsch" } @article{jame:92, author = "D. James", year = "1992", title = "Implicit Nullspace Iterative Methods for Constrained Least Squares Problems", journal = "SIAM J. Matrix. Anal. Appl.", volume = "13", pages = "962--978", kwds = "iter, constr, sparse" } @article{jawo:77, author = "M. Jankowski and H. Wozniakowski", year = "1977", title = "Iterative Refinement Implies Numerical Stability", journal = "BIT", volume = "17", pages = "303--311", kwds = "ir" } @article{jeaj:84, author = "A. Jennings and M. A. Ajiz", year = "1984", title = "Incomplete Methods for Solving {$A^TAx=b$}", journal = "SIAM J. Sci. Statist. Comput.", volume = "5", pages = "978--987", kwds = "cg, precond" } @article{jeos:74, author = "L. S. Jennings and M. R. Osborne", year = "1974", title = "A Direct Error Analysis for Least Squares", journal = "Numer. Math.", volume = "22", pages = "322--332", kwds = "err" } @techreport{jeso:92, author = "E. Jessup and D. C. Sorenson", year = "1992", title = "A Parallel Algorithm for Computing the Singular Value Decomposition of a Matrix", institution = "Department of Computer Science, University of Colorado", address = "Boulder, CO", type = "{Tech. Report}", number = "CU-CS-623-92", kwds = "svd, prll", } @article{jin:96, author = "X.-Q. Jin", year = "1996", title = "A Preconditioner for Constrained and Weighted Least Squares Problems with {Toeplitz} Structure", journal = "BIT", volume = "36", pages = "101--109", kwds = "toepl, cg, precond" } @article{jodm:63, author = "D.~M. Johnson and A.~L. Dulmage and N.~S. Mendelsohn", year = "1963", title = "Connectivity and Reducibility of Graphs", journal = "Canad. J. Math.", volume = "14", pages = "529--539", kwds = "sparse, graph " } @article{jord:68, author = "T. L. Jordan", year = "1968", title = "Experiments on Error Growth Associated with some Linear Least-squares Procedures", journal = "Math. Comp.", volume = "22", pages = "579--588", kwds = "grsch" } ka- @article{kacz:37, author = "S. Kaczmarz", year = "1937", title = "Angen{\"a}herte {Aufl{\"o}sung} von {Systemen} linearer {Gleichungen}", journal = "Bulletin Internat. Acad. Polon. Sciences et Lettres", pages = "355--357", kwds = "iter" } @article{kaha:66, author = "W. Kahan", year = "1966", title = "Numerical Linear Algebra", journal = "Canad. Math. Bull.", volume = "9", pages = "757--801", kwds = "nla, cond, survey" } @techreport{kaha:66a, author = "W. Kahan", year = "1966", title = "Accurate Eigenvalues of a Symmetric Tridiagonal Matrix", institution = "Computer Science Department, Stanford University", address = "CA", type = "{Tech. Report}", number = "CS-41", note = "{Revised June 1968}", kwds = "geig, regul" } @article{kasa:89, author = "C. Kamath and A. Sameh", year = "1988/89", title = "A Projection Method for Solving Nonsymmetric Linear Systems on Multiprocessors", journal = "Parallel Computing", volume = "9", pages = "291--312", kwds = "iter, prll" } @article{kara:74, author = "I. Karasalo", year = "1974", title = "A Criterion for Truncation of the {QR} Decomposition Algorithm for the Singular Linear Least Squares Problem", journal = "BIT", volume = "14", pages = "156--166", kwds = "cond, rank" } @article{kauf:75, author = "L. Kaufman", year = "1975", title = "Variable Projection Methods for Solving Separable Nonlinear Least Squares Problems", journal = "BIT", volume = "15", pages = "49--57", kwds = "nlsq, varpro" } @article{kauf:79, author = "L. Kaufman", year = "1979", title = "Application of Dense {Householder} Transformation to a Sparse Matrix", journal = "ACM Trans. Math. Software", volume = "5", pages = "442--450", kwds = "sparse, qrd" } @article{kauf:87, author = "L. Kaufman", year = "1987", title = "The Generalized {Householder} Transformation and Sparse Matrices", journal = "Linear Algebra Appl.", volume = "90", pages = "221--234", kwds = "sparse, qrd" } @article{kape:78, author = "L. Kaufman and V. Pereyra", year = "1978", title = "A method for Separable Nonlinear Least Squares Problems with Separable Nonlinear Equality Constraints", journal = "SIAM J. Numer. Anal.", volume = "15", pages = "12--20", kwds = "nlsq, varpro" } @article{kasy:92, author = "L. Kaufman and G. Sylvester", year = "1992", title = "Separable Nonlinear Least Squares Problems with Multiple Right Hand Sides", journal = "SIAM J. Matrix Anal. Appl.", volume = "13", pages = "68--89", kwds = "nlsq, varpro" } @article{kell:65, author = "J. Keller", year = "1965", title = "On the Solution of Singular and Semidefinite Linear Systems by Iterations", journal = "J. Soc. Indust. Appl. Math. Ser. B ", volume = "2", pages = "281--290", kwds = "iter, ginv" } @article{kija:74, author = "A. Kie{\l}basi\'nski and J. Jankowska", year = "1974", title = "Fehleranalyse der {Schmidtschen} und {Powellschen Orthonormalisierungsverfahren}", journal = "ZAMM", volume = "54", pages = "223", kwds = "err,grsch " } @book{kisc:88, author = "A. Kie{\l}basi\'nski and H. Schwetlick", year = "1988", title = "Numerische Lineare {Algebra}", publisher = "VEB Deutscher Verlag der Wissenschaften", address = "Berlin", kwds = "survey " } @article{kogb:55, author = "E. G. Kogbetliantz", year = "1955", title = "Solution of Linear Equations by Diagonalization of Coefficients Matrix", journal = "Quart. Appl. Math.", volume = "13", pages = "123--132", kwds = "svd, jacobi" } @article{kola:78, author = "G. B. Kolata", year = "1978", title = "Geodesy: Dealing with an Enormous Computer Task", journal = "Science", volume = "200", pages = "421--422", kwds = "sparse, geod" } @article{kopa:81, author = "S. Kourouklis and C. C. Paige", year = "1981", title = "A Constrained Approach to the General {Gauss-Markov} Linear Model", journal = "J. Amer. Statist. Assoc.", volume = "76", pages = "620-625", kwds = "stat, regr, glsq, constr" } @article{kova:70, author = "Z. V. Kovarik", year = "1970", title = "Some Iterative Methods for Improving Orthonormality", journal = "SIAM J. Numer. Anal.", volume = "7", pages = "386--389", kwds = "orth" } @article{krog:74, author = "F. T. Krogh", year = "1974", title = "Efficient Implementation of a Variable Projection Algorithm for Nonlinear Least Squares", journal = "Comm. ACM", volume = "17", pages = "167--169", kwds = "nlsq, varpro" } la- @book{lati:85, author = "P. Lancaster and M. Tismenetsky", year = "1985", title = "The Theory of Matrices", publisher = "Academic Press", address = "New York", notes = "Second Ed.", kwds = "survey" } @article{lanc:50, author = "C. Lanczos", year = "1950", title = "An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators", journal = "J. Res. Nat. Bur. Standards", volume = "45", pages = "255--282", kwds = "svd, eigv" } @book{lanc:61, author = "C. Lanczos", year = "1961", title = "Linear Differential Operators", publisher = "D. Van Nostrand", address = "London, UK", kwds = "svd" } @article{land:51, author = "L. Landweber", year = "1951", title = "An iterative formula for {Fredholm} integral equations of the first kind", journal = "Amer. J. Math.", volume = "73", pages = "615--624", kwds = "iter,illp" } @book{lapl:1816, author = "P. S. Laplace", year = "1816", title = "Th\'eorie analytique des probabilit\'es. Premier suppl\'ement, {\rm 3rd ed.}", publisher = "Courcier", address = "Paris", notes = "with an introduction and three supplements", kwds = "hist" } @phdthesis{laws:61, author = "C. L. Lawson", year = "1961", title = "Contributions to the Theory of Linear Least Maximum Approximation", school = "UCLA", address = "Los Angeles, CA", type = "{Ph. D.} thesis", kwds = "" } @techreport{laws:73, author = "C. L. Lawson", year = "1973", title = "Sparse Matrix Methods Based on Orthogonality and Conjugacy", institution = "Jet Propulsion Lab., Cal. Inst. of Tech.", address = "Pasadena, CA", type = "Tech. Mem.", number = "33-627, June 1973", kwds = "nla, soft, blas" } @book{laha:74, author = "C. L. Lawson and R. J. Hanson", year = "1974", title = "Solving Least Squares Problems", publisher = "Prentice Hall", address = "Englewood Cliffs, NJ", kwds = "qrd, pert, survey" } @book{laha:95, author = "C. L. Lawson and R. J. Hanson", year = "1995", title = "Solving Least Squares Problems", series = "Classics in Applied Mathematics", publisher = "SIAM", address = "Philadelphia", kwds = "survey" } @article{lhkk:79, author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T. Krogh", year = "1979", title = "Basic Linear Algebra Subprograms for {Fortran} Usage", journal = "ACM Trans. Math. Software", volume = "5", pages = "308-323", kwds = "nla, soft, blas" } le- @book{lege:1805, author = "A. M. Legendre", year = "1805", title = "Nouvelles m\'ethodes pour la d\'etermination des orbites des com\`etes", publisher = "Courcier", address = "Paris", kwds = "hist" } @article{leme:75, author = "F. Lemeire", year = "1975", title = "Bounds for Condition Numbers of Triangular and Trapezoid Matrices", journal = "BIT", volume = "15", pages = "58--64", kwds = "cond" } @techreport{lewe:70, author = "{\"O}. Leringe and P.-{\AA}. Wedin", year = "1970", title = "A Comparison between Different Methods to Compute a Vector $x$ which Minimizes {$\|Ax-b\|_2$} when {$Gx=h$}", institution = "Department of Computer Science, Lund University", address = "Lund, Sweden", type = "{Tech. Report}", kwds = "constr" } @article{leve:44, author = "K. Levenberg", year = "1944", title = "A Method for the Solution of Certain Non-Linear Problems in Least Squares", journal = "Quart. Appl. Math.", volume = "2", pages = "164--168", kwds = "nlsq, regul" } @techreport{lepw:89, author = "J. G. Lewis and D. J. Pierce and D. K. Wah", year = "1989", title = "Multifrontal {Householder} {QR} Factorization", institution = "Boeing Computer Services", address = "Seattle, WA", type = "{Tech. Report}", number = "ECA-TR-127-Revised", kwds = "sparse, qrd" } li- @techreport{li:93, author = "Y. Li", year = "1993", title = "Solving $l_p$ Problems and Applications", institution = "Advanced Computing Research Institute, Cornell University", address = "Ithaca, NY", type = "{Tech. Report}", number = "CTC93TR122, 03/93", kwds = "rob" } @article{li:93a, author = "Y. Li", year = "1993", title = "A Globally Convergent Method for $l_p$ Problems", journal = "SIAM J. Optim.", volume = "3", pages = "609--629", kwds = "rob" } @techreport{lirz:95, author = "T. Y. Li and N. H. Rhee and Z. Zeng", year = "1995", title = "An Efficient and Accurate Parallel Algorithm for the Singular Value Problem of Bidiagonal Matrices", institution = "Department of Mathematics, University of Missouri--Kansas City", type = "{Tech. Report}", kwds = "svd" } @article{licr:85, author = "Y. Lin and C. W. Cryer", year = "1985", title = "An Alternating Direction Implicit Algorithm for the Solution of Linear Complementarity Problems Arising From Free Boundary Problems", journal = "J. Appl. Math. Optim.", volume = "13", pages = "1--17", kwds = "constr" } @article{lipa:87, author = "Y. Lin and J. S. Pang", year = "1987", title = "Iterative Methods for Large Convex Quadratic Programs: A Survey", journal = "SIAM J. Control Optim.", volume = "25", pages = "383--411", kwds = "constr" } @techreport{lind:82, author = "P. Lindstr{\"o}m", year = "1982", title = "A Stabilized {Gauss-Newton} Algorithm for Unconstrained Nonlinear Least Squares Problems", institution = "Institute of Information Processing, University of Ume{\aa}", address = "Sweden", type = "{Tech. Report}", number = "UMINF--102.82", kwds = "nlsq" } @techreport{lind:83, author = "P. Lindstr{\"o}m", year = "1983", title = "A General Purpose Algorithm for Nonlinear Least Squares Problems with Nonlinear Constraints", institution = "Institute of Information Processing, University of Ume\aa", address = "Sweden", type = "{Tech. Report}", number = "UMINF--102.83", kwds = "nlsq, constr" } @techreport{lind:84, author = "P. Lindstr{\"o}m", year = "1984", title = "Two user guides, one ({ENLSIP}) for constrained --- one ({ELSUNC}) for unconstrained nonlinear least squares problems", institution = "Institute of Information Processing, University of Ume\aa", address = "Sweden", type = "{Tech. Report}", number = "UMINF--109.82 and 110.84", kwds = "nlsq, constr, soft" } @article{liwe:84, author = "P. Lindstr{\"o}m and P.-{\AA}. Wedin", year = "1984", title = "A New Linesearch Algorithm for Unconstrained Nonlinear Least Squares Problems", journal = "Math. Programming", volume = "29", pages = "268--296", kwds = "nlsq" } @techreport{liwe:86, author = "P. Lindstr{\"o}m and P.-{\AA}. Wedin", year = "1986", title = "Methods and Software for Nonlinear Least Squares Problems", institution = "Institute of Information Processing, University of Ume\aa", address = "Sweden", type = "{Tech. Report}", number = "UMINF--133.87", kwds = "nlsq, soft" } @book{linn:61, author = "I. Linnik", year = "1961", title = "Method of Least Squares and Principles of the Theory of Observations", publisher = "Pergamon Press", address = "New York", kwds = "stat, survey" } @article{lirt:79, author = "R. J. Lipton and D. J. Rose and R. E. Tarjan", year = "1979", title = "Generalized Nested Dissection", journal = "SIAM J. Numer. Anal. ", volume = "16", pages = "346--358", kwds = "sparse, nestdis" } @article{liu:86, author = "J. W.-H. Liu", year = "1986", title = "On General Row Merging Schemes for Sparse {Givens} Transformations", journal = "SIAM J. Sci. Statist. Comput. ", volume = "7", pages = "1190--1211", kwds = "sparse, rot, multfr" } @article{liu:90, author = "J. W.-H. Liu", year = "1990", title = "The Role of Elimination Trees in Sparse Factorization", journal = "SIAM J. Matrix Anal. Appl.", volume = "11", pages = "134--172", kwds = "sparse, multfr" } @article{liu:92, author = "J. W.-H. Liu", year = "1992", title = "The Multifrontal Method for Sparse Matrix Solution: {Theory} and Practice", journal = "SIAM Review", volume = "34", pages = "82--109", kwds = "sparse, multfr" } lo- @article{long:81, author = "J. W. Longley", year = "1981", title = "Modified {Gram-Schmidt} Process vs. Classical {Gram-Schmidt}", journal = "Comm. Statist. Simulation Comput.", volume = " B10, 5", pages = "517--527", kwds = "grsch" } @book{long:84, author = "J. W. Longley", year = "1984", title = "Least Squares Computations Using Orthogonal Methods", publisher = "Marcel Dekker", address = "New York", kwds = "orth, grsch, survey" } @incollection{loui:87, author = "A. K. Louis", year = "1987", title = "Convergence of the Conjugate Gradient Method for Compact Operators", booktitle = "Inverse and Ill-posed Problems", editor = "H. W. Engl and C. W. Groetsch", publisher = "Academic Press, New York", pages = "177--183", kwds = "sparse, augms" } @techreport{luba:93, author = "S. -M. Lu and J. L. Barlow", year = "1993", title = "Computation of Orthogonal Factors of Sparse Matrices", institution = "Department of Computer Science, The Pennsylvania State University", address = "State College, PA", type = "{Tech. Report}", number = "CSE-93-014", kwds = "sparse, qrd" } @article{luk:80, author = "F. T. Luk", year = "1980", title = "Computing the Singular Value Decomposition on the {ILLIAC IV}", journal = "ACM Trans. Math. Software", volume = "6", pages = "524--539", kwds = "prll, svd" } @article{luk:85, author = "F. T. Luk", year = "1985", title = "A Parallel Method for Computing the Generalized Singular Value Decomposition", journal = "J. Parallel Distributed Comput.", volume = "2", pages = "250--260", kwds = "prll, gsvd" } @article{luk:86, author = "F. T. Luk", year = "1986", title = "A Rotation Method for Computing the {QR}-Decomposition", journal = "SIAM J. Sci. Statist. Comput.", volume = "7", pages = "452--459", kwds = "prll, qrd, rot" } @article{luqi:87, author = "F. T. Luk and S. Qiao", year = "1987", title = "A Fast but Unstable Orthogonal Triangularization Technique for {Toeplitz} Matrices", journal = "Linear Algebra Appl.", volume = "88/89", pages = "495--506", kwds = "toep, qrd" } @article{luqi:94, author = "F. T. Luk and S. Qiao", year = "1994", title = "A New Matrix Decomposition for Signal Processing", journal = "Automatica", volume = "30", pages = "39--43", kwds = "upd, gqrd, sigp" } @article{lums:91, author = "I. Lustig and R. Marsten and D. Shanno", year = "1991", title = "Computational Experience with a Primal-Dual Interior Point Method for Linear Programming", journal = "Linear Algebra Appl.", volume = "152", pages = "191--222", kwds = "constr" } @article{lauc:59, author = "P. L{\"a}uchli", year = "1959", title = "{Iterative L\"osung und Fehlerabsch\"atzung in der Ausgleichrechnung}", journal = "ZAMP", volume = "10", pages = "245--280", kwds = "iter, precond, err" } @article{lauc:61, author = "P. L{\"a}uchli", year = "1961", title = "{Jordan-Elimination und Ausgleichung nach kleinsten Quadraten}", journal = "Numer. Math.", volume = "3", pages = "226--240", kwds = "iter, precond" } @article{lots:83, author = "P. L{\"o}tstedt", year = "1983", title = "Perturbation Bounds for the Linear Least Squares Problem Subject to Linear Inequality Constraints", journal = "BIT", volume = "23", pages = "500--519", kwds = "pert, constr" } @article{lots:84, author = "P. L{\"o}tstedt", year = "1984", title = "Solving the Minimal Least Squares Problem Subject to Bounds on the Variables", journal = "BIT", volume = "24", pages = "206--224", kwds = "constr, rank" } ma- @article{mani:90, author = "K. Madsen and H. B. Nielsen", year = "1990", title = "Finite Algorithms for Robust Regression", journal = "BIT", volume = "30", pages = "682--699", kwds = "rob" } @article{mani:93, author = "K. Madsen and H. B. Nielsen", year = "1993", title = "A Finite Smoothing Algorithm for Linear $l_1$ Estimation", journal = "SIAM J. Optim.", volume = "3", pages = "68--80", kwds = "rob" } @phdthesis{mahd:81, author = "N. Mahdavi-Amiri", year = "1981", title = "Generally Constrained Nonlinear Least Squares and Generating Test Problems: Algorithmic Approach", school = "The John Hopkins University", address = "Baltimore, MD", type = "{Ph. D.} thesis", kwds = "nlsq, constr" } @book{main:84, author = "J. H. Maindonald", year = "1984", title = "Statistical Computation", publisher = "John Wiley", address = "New York", kwds = "stat, survey" } @phdthesis{mann:85, author = "P. Manneback", year = "1985", title = "On Some Numerical Methods for Solving Large Sparse Linear Least Squares Problems", school = "Facult\'es Universitaires Notre-Dame de la Paix", address = "Namur, Belgium", type = "{Ph. D.} thesis", kwds = "sparse, thesis" } @phdthesis{mala:92, author = "J. Malard", year = "1992", title = "Block Solvers for Dense Linear Systems On Local Memory Multiprocessors", school = "School of Computer Science, McGill University", address = "Montr\'eal, Canada", type = "{Ph. D.} thesis", kwds = "sparse, thesis" } @article{mamt:85, author = "P. Manneback and C. Murigande and P. L. Toint", year = "1985", title = "A Modification of an Algorithm by {Golub} and {Plemmons} for Large Linear Least Squares in the Context of {Doppler} Positioning", journal = "IMA J. Numer. Anal.", volume = "5", pages = "221--234", kwds = "iter, basys" } @techreport{mant:79, author = "T. A. Manteuffel", year = "1979", title = "Numerical Rank Determination in Linear Least Squares Problems", institution = "Sandia Laboratories", address = " Albuquerque, NM", type = "{Tech. Report}", number = "SAND 79-8243", kwds = "rank, err" } @article{mant:80, author = "T. A. Manteuffel", year = "1980", title = "An Incomplete Factorization Technique for Positive Definite Linear Systems", journal = "Math. Comp.", volume = "34", pages = "473--497", kwds = "iter, precond" } @article{mant:81, author = "T. A. Manteuffel", year = "1981", title = "An Interval Analysis Approach to Rank Determination in Linear Least Squares Problems", journal = "SIAM J. Sci. Statist. Comp.", volume = "2", pages = "335--348", kwds = "rank, err" } @article{manp:85, author = "T. L. Markham and M. Neumann and R. J. Plemmons", year = "1985", title = "Convergence of a Direct-Iterative Method for Large-Scale Least-squares Problems", journal = "Linear Algebra Appl.", volume = "69", pages = "155--167", kwds = "iter, precond" } @book{mark:12, author = "A. A. Markoff", year = "1912", title = "Wahrscheinlichheitsrechnung, {\rm 2nd. ed., H. Liebmann, Trans.}", address = "Leipzig", kwds = "stat" } @article{mark:57, author = "H. M. Markowitz", year = "1957", title = "The Elimination Form of the Inverse and its Application to Linear Programming", journal = "Management Sci.", volume = "3", pages = "255--269", kwds = "sparse, perm" } @article{marq:63, author = "D. W. Marquardt", year = "1963", title = "An Algorithm for Least-Squares Estimation of Nonlinear Parameters", journal = "J. Soc. Indust. Appl. Math.", volume = "11", pages = "431--441", kwds = "nlsq, regul" } @article{mart:87, author = "J. M. Martinez", year = "1987", title = "An Algorithm for Solving Sparse Nonlinear Least Squares Problems", journal = "Computing", volume = "39", pages = "307--325", kwds = "iter, sparse, nlsq" } @phdthesis{mats:91, author = "P. MATSTOMS", year = "1991", title = "The Multifrontal Solution of Sparse Linear Least Squares Problems", school = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", type = "{Licentiat} thesis", kwds = "sparse, qrd, multfr" } @techreport{mats:92, author = "P. Matstoms", year = "1992", title = "{QR}{\rm 27}---{Specification} Sheet", type = "{Tech. Report}", institution = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", number = "March 1992", kwds = "sparse, qrd, softw" } @phdthesis{mats:94, author = "P. MATSTOMS", year = "1994", title = "Sparse {QR} Factorization with Applications to Linear Least Squares Problems", school = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", type = "{Ph. D.} thesis", kwds = "sparse, qrd, multfr" } @article{mats:94a, author = "P. MATSTOMS", year = "1994", title = "Sparse {QR} Factorization in {MATLAB}", journal = "ACM Trans. Math. Software", volume = "20", pages = "136--159", kwds = "sparse, qrd, multfr" } @article{mats:95, author = "P. Matstoms", year = "1995", title = "Parallel Sparse {QR} Factorization on Shared Memory Architectures", journal = "Parallel Comput.", volume = "21", pages = "473--486", kwds = "sparse, qrd, multfr,prll" } @article{mevo:77, author = "J. A. Meijerink and H. van der Vorst", year = "1977", title = "An Iterative Method for Linear Systems of which the Coefficient Matrix is a Symmetric {M}-matrix", journal = "Math. Comp.", volume = "31", pages = "148--162", kwds = "iter, precond" } @article{mein:83, author = "J. Meinguet", year = "1983", title = "Refined Error Analysis of {Cholesky} Factorization", journal = "SIAM J. Numer. Anal.", volume = "20", pages = "1243--1250", kwds = "err, chol" } @techreport{meis:80, author = "P. Meissl", year = "1980", title = "A Priori Prediction of Roundoff Error Accumulation in the Solution of a Super-Large Geodetic Normal Equation System", institution = "National Oceanic and Atmospheric Administration", type = "Professional Paper", number = "12", kwds = "geod, err, ne" } mi- mo- @article{mirs:60, author = "L. Mirsky", year = "1960", title = "Symmetric Gauge Functions and Unitarily Invariant Norms", journal = "Quart. J. Math. Oxford", volume = "11", pages = "50--59", kwds = "nla, max" } @article{mocl:84, author = "J. J. Modi and M. R. B. Clarke", year = "1984", title = "An Alternate {Givens} Ordering", journal = "Numer. Math.", volume = "43", pages = "83--90", kwds = "prll, rot" } @article{mole:67, author = "C. B. Moler", year = "1967", title = "Iterative Refinement in Floating Point", journal = "J. Assoc. Comput. Mach.", volume = "14", pages = "316--321", kwds = "ir" } @incollection{moli:77, author = "L. Molinari", year = "1977", title = "{Gram-Schmidt'sches Orthogonalisierungsverfahren}", booktitle = "{Numerische Prozeduren aus Nachlass und Lehre von Prof. Heinz Rutishauser}", editor = "W. Gander and L. Molinari and H. Svecov\'a", pages = "77--93", publisher = "Birkh{\"a}user, Stuttgart", kwds = "grsch, orth" } @article{movd:93, author = "M. Moonen and P. {Van Dooren}", year = "1993", title = "On the {QR} Algorithm and Updating the {SVD} and {URV} Decompositions in Parallel", journal = "Linear Algebra Appl.", volume = "188/189", pages = "549--568", kwds = "upd, svd, qrd" } @article{movv:92, author = "M. Moonen and P. {Van Dooren} and J. Vandewalle", year = "1992", title = "An {SVD} Updating Algorithm for Subspace Tracking", journal = "SIAM J. Matrix Anal. Appl.", volume = "13", pages = "1015--1038", kwds = "upd, sigp, svd" } @article{mosg:90, author = "R. Morandi and F. Sgallari", year = "1990", title = "Parallel Algorithms for the Iterative Solution of Sparse Least-Squares Problems", journal = "Parallel Comput.", volume = "13", pages = "271--280", kwds = "iter, prll" } @inproceedings{more:78, author = "J. J. Mor\'e", year = "1978", title = "The {Levenberg-Marquardt} Algorithm: Implementation and Theory", booktitle = "Numerical Analysis. Proceedings Biennial Conference Dundee 1977", editor = "G. A. Watson", pages = "105--116", publisher = "Springer-Verlag, Berlin", series = " Lecture Notes in Mathematics", volume = "630", kwds = "nlsq" } @inproceedings{more:83, author = "J. J. Mor\'e", year = "1983", title = "Recent Developments in Algorithms and Software for Trust Region-methods", booktitle = "Mathematical Programming. The State of the Art, Proceedings Bonn 1982", editor = "A. Bachem and M. Gr{\"o}tchel and B. Korte", pages = "258--287", publisher = "Springer-Verlag, Berlin", kwds = "nlsq, soft, survey" } @article{moto:89, author = "J. J. Mor\'e and G. Toraldo", year = "1989", title = "Algorithms for Bound Constrained Quadratic Programming Problems", journal = "Numer. Math.", volume = "55", pages = "377--400", kwds = "nlsq, soft, survey" } @techreport{mogh:80, author = "J. J. Mor\'e and B. S. Garbow and K. E. Hillstrom", year = "1980", title = "Users' Guide for {MINPACK}-{\rm 1}", institution = "Applied Math. Div., Argonne National Laboratory", address = "Argonne, IL", type = "{Tech. Report}", number = "ANL-80-74", note = "", kwds = "nlsq, soft" } @book{mowr:93, author = "J. J. Mor\'e and S.~J.~Wright", year = "1993", title = "Optimization Software Guide", publisher = "SIAM", address = "Philadelphia", kwds = "opt, nlsq, soft, survey" } @book{moor:35, author = "E. H. Moore", year = "1935", title = "General Analysis. Part I", publisher = "American Philosophical Society", address = "Philadelphia", kwds = "ginv" } @article{moso:81, author = "J. J. Mor\'e and D. C. Sorenson", year = "1981", title = "Computing a Trust Region Step", journal = "SIAM J. Sci. Statist. Comput.", volume = "4", pages = "553--572", kwds = "nlsq, regul" } @article{munk:80, author = "N. Munksgaard", year = "1980", title = "Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients", journal = "ACM Trans. Math. Software", volume = "6", pages = "206--219", kwds = "sparse, cg, iter, precond" } na- @phdthesis{nagy:91, author = "J. G. Nagy", year = "1991", title = "{Toeplitz} Least Squares Computations", school = "North Carolina State University", address = "Raleigh, NC", type = "{Ph. D.} thesis", kwds = "toep" } @article{nagy:93, author = "J. G. Nagy", year = "1993", title = "Fast Inverse {QR} Factorization for {Toeplitz} Matrices", journal = "SIAM J. Sci. Comput.", volume = "14", pages = "1174--1193", kwds = "qrd, toep" } @article{nash:75, author = "J. C. Nash", year = "1975", title = "A One-sided Transformation Method for the Singular Value Decomposition and Algebraic Eigenproblem", journal = "Comput. J.", volume = "18", pages = "74--76", kwds = "svd, jacobi" } @book{nash:76, editor = "M. Z. Nashed", year = "1976", title = "Generalized Inverses and Applications", publisher = "Academic Press", address = "New York", kwds = "ginv" } @article{naza:80, author = "L. Nazareth", year = "1980", title = "Some Recent Approaches to Solving Large Residual Nonlinear Least Squares Problems", journal = "SIAM Review", volume = "22", pages = "1--11", kwds = "nlsq" } @article{nemi:86, author = "A. S. Nemirovskii", year = "1986", title = "The Regularization Properties of the Adjoint Gradient Method in Ill-Posed Problems", journal = "USSR Comput. Math. and Math. Phys.", volume = "26:2", pages = "7--16", kwds = "cg, regul" } @article{neum:95, author = "A. Neumaier", year = "1995", title = "Hybrid Norms and Bounds for Overdetermined Linear Systems", journal = "Linear Algebra Appl.", volume = "216", pages = "257--265", kwds = "err" } @article{nipv:84, author = "W. Niethammer and J. de Pillis and R. S. Varga", year = "1984", title = "Convergence of Block Iterative Methods Applied to Sparse Least-squares Problems", journal = "Linear Algebra Appl.", volume = "58", pages = "327--341", kwds = "iter,precond" } @article{ng:91, author = "E. G. Ng", year = "1991", title = " A Scheme for Handling Rank Deficiency in the Solution of Sparse Linear Least Squares Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "12", pages = "1173--1183", kwds = "nlsq" } @inproceedings{nobl:76, author = "B. Noble", year = "1976", title = "Methods for Computing the {Moore-Penrose} Generalized Inverse and Related Matters", pages = "245--301", booktitle = "Generalized Inverses and Applications. Proceedings of an Advanced Seminar, The University of Wisconsin-Madison, Oct. 1973", editor = "M. Z. Nashed", publisher = "Academic Press, New York", kwds = "ginv" } @article{oepr:64, author = "W. Oettli and W. Prager", year = "1964", title = "Compatibility of Approximate Solution of Linear Equations with Given Error Bounds for Coefficients and Right-Hand Sides", journal = "Numer. Math.", volume = "6", pages = "405--409", kwds = "nla, pert, pert, err" } -ol @article{olea:80, author = "D. P. O'Leary", year = "1980", title = "A Generalized Conjugate Gradient Algorithm for Solving Class of Quadratic Programming Problems", journal = "Linear Algebra Appl.", volume = "34", pages = "371--399", kwds = "cg, iter, quadpr" } @article{olea:80a, author = "D. P. O'Leary", year = "1980", title = "Estimating Matrix Condition Numbers", journal = "SIAM J. Sci. Statist. Comput.", volume = "1", pages = "205--209", kwds = "cond" } @article{olea:90, author = "D. P. O'Leary", year = "1990", title = "On Bounds For Scaled Projections and Pseudo-Inverses", journal = "Linear Algebra Appl.", volume = "132", pages = "115--117", kwds = "wlsq, ginv" } @article{olea:90a, author = "D. P. O'Leary", year = "1990", title = "Robust Regression Computation Using Iteratively Reweighted Least Squares", journal = "SIAM J. Matrix Anal. Appl.", volume = "11", pages = "466--480", kwds = "rob, regr, iter" } @article{olru:86, author = "D. P. O'Leary and B. W. Rust", year = "1986", title = "Confidence Intervals for Inequality-Constrained Least Squares Problems, with Applications to Ill-Posed Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "7", pages = "473--489", kwds = "err, illp, constr" } @article{olsi:81, author = "D. P. O'Leary and J. A. Simmons", year = "1981", title = "A Bidiagonalization-regularization Procedure for Large Scale Discretizations of Ill-posed Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "2", pages = "474--489", kwds = "iter, lanczos" } @article{olwh:90, author = "D. P. O'Leary and P. Whitman", year = "1990", title = "Parallel {QR} Factorization by {Householder} and Modified {Gram-Schmidt} Algorithms", journal = "Parallel Comput.", volume = "16", pages = "99--112", kwds = "qrd, grsch, prll" } @article{ollb:94, author = "S. J. Olszanskyj and J. M. Lebak and A. Bojanczyk", year = "1994", title = "Rank-$k$ Modification Methods for Recursive Least Squares Problems", journal = "Numer. Algorithms", volume = "7", pages = "325--354", kwds = "block, upd, sigp, rls" } or- @phdthesis{oreb:86, author = "U. Oreborn", year = "1986", title = "A Direct Method for Sparse Nonnegative Least Squares Problems", school = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", type = "{Licentiat} thesis", number = "87", kwds = "sparse, constr, qrd, soft" } @book{orrh:70, author = "J. M. Ortega and W. C. Rheinboldt", year = "1970", title = "Iterative Solution of Nonlinear Equations in Several Variables", publisher = "Academic Press", address = "New York", kwds = "iter, nlsq, survey" } @article{osbo:61, author = "E. E. Osborne", year = "1961", title = "On Least Squares Solutions of Linear Equations", journal = "J. Assoc. Comput. Mach.", volume = "8", pages = "628--636", kwds = "nla" } @article{osbo:76, author = "E. E. Osborne", year = "1976", title = "Nonlinear Least Squares---the {Levenberg} Algorithm Revisited", journal = "J. Austral. Math. Soc., Ser. B", volume = "19", pages = "343--357", kwds = "nlsq" } @article{osbo:76a, author = "M. R. Osborne", year = "1976", title = "On the Computation of Stepwise Regressions", journal = "Austral. Comput. J.", volume = "8", pages = "61--63", kwds = "stat, regr" } @incollection{osbo:76b, author = "M. R. Osborne", year = "1976", title = "Some Aspects of Nonlinear Least Squares Calculations", booktitle = "Numerical Methods for Nonlinear Optimization", editor = "F. A. Lootsma", pages = "171--189", publisher = "Academic Press, New York", kwds = "nlsq, opt" } @book{osbo:85, author = "M. R. Osborne", year = "1985", title = "Finite Algorithms in Optimization and Data Analysis", publisher = "John Wiley", address = "New York", kwds = "nlsq, opt, survey" } @techreport{osbo:94, author = "M. R. Osborne", year = "1994", title = "Solving Least Squares Problems on Parallel Vector Processors", institution = "School of Mathematical Sciences, Australian National University", address = "Canberra", type = "{Tech. Report}", number = "", kwds = "stat, regr" } @book{oszl:83, author = "O. {\O}sterby and Z. Zlatev", year = "1983", title = "Direct Methods for Sparse Matrices", series = "Lecture Notes in Computer Science", volume = "157", publisher = "Springer-Verlag", address = "Berlin", kwds = "sparse, survey" } @article{ostr:87, author = "G. Ostrouchov", year = "1987", title = "Symbolic {Givens} Reduction and Row-ordering in Large Sparse Least Squares Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "8", pages = "248--264", kwds = "sparse, perm, rot" } @phdthesis{paig:71, author = "C. C. Paige", year = "1971", title = "The Computation of Eigenvalues and Eigenvectors of Very Large Sparse Matrices", school = "University of London, UK", type = "{Ph. D.} thesis", kwds = "sparse, lanczos, iter, thesis" } @article{paig:73, author = "C. C. Paige", year = "1973", title = "An Error Analysis of a Method for Solving Matrix Equations", journal = "Math. Comp.", volume = "27", pages = "355--359", kwds = "err, uds" } @article{paig:74, author = "C. C. Paige", year = "1974", title = "Bidiagonalization of Matrices and Solution of Linear Eqautions", journal = "SIAM J. Numer. Anal.", volume = "11", pages = "197--209", kwds = "bid, iter" } @article{paig:76, author = "C. C. Paige", year = "1976", title = "Error Analysis of the {Lanczos} Algorithm for Tridiagonalizing a Symmetric Matrix", journal = "J. Inst. Math. Applic.", volume = "18", pages = "341--349", kwds = "lanczos" } @article{paig:78, author = "C. C. Paige", year = "1978", title = "Numerically Stable Computations for General Univariate Linear Models", journal = "Comm. Statist.", volume = "B7", pages = "437--453", kwds = "stat, regr, glsq, upd" } @article{paig:79, author = "C. C. Paige", year = "1979", title = "Computer Solution and Perturbation Analysis of Generalized Linear Least Squares Problems", journal = "Math. Comp.", volume = "33", pages = "171-184", kwds = "regr, pert, glsq, pert" } @article{paig:79a, author = "C. C. Paige", year = "1979", title = "Fast Numerically Stable Computations for Generalized Least Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "16", pages = "165--171", kwds = "nla, glsq" } @article{paig:80, author = "C. C. Paige", year = "1980", title = "Error Analysis of Some Techniques for Updating Orthogonal Decompositions", journal = "Math. Comp.", volume = "34", pages = "465-471", kwds = "qrd, upd, downd, err" } @article{paig:81, author = "C. C. Paige", year = "1981", title = "Properties of Numerical Algorithms Related to Computing Controllability", journal = "IEEE Trans. Automat. Control", volume = "26", pages = "130--138", kwds = "contr" } @article{paig:84, author = "C. C. Paige", year = "1984", title = "A Note on a Result of {Sun Ji-guang}: Sensitivity of the {CS} and {GSV} Decomposition", journal = "SIAM J. Numer. Anal.", volume = "21", pages = "186-191", kwds = "pert, csd, gsvd" } @article{paig:85, author = "C. C. Paige", year = "1985", title = "The General Linear Model and the Generalized Singular Value Decomposition", journal = "Linear Algebra Appl.", volume = "70", pages = "269--284", kwds = "glsq, gsvd" } @article{paig:86, author = "C. C. Paige", year = "1986", title = "Computing the Generalized Singular Value Decomposition", journal = "SIAM J. Sci. Statist. Comput.", volume = "7", pages = "1126--1146", kwds = "gsvd, jacobi" } @inproceedings{paig:90, author = "C. C. Paige", year = "1990", title = "Some Aspects of Generalized {QR} Factorizations", pages = "71--91", booktitle = "Reliable Numerical Computation", editor = "M. G. Cox and S. J. Hammarling", publisher = "Clarendon Press, Oxford, UK", kwds = "gqrd" } @article{paig:94, author = "C. C. Paige", year = "1994", title = "History and Generality of the {CS}-Decomposition", journal = "Linear Algebra Appl.", volume = "208/209", pages = "303--326", kwds = "glsq, gsvd" } @article{pang:82, author = "J. -S. Pang", year = "1982", title = "On the Convergence of a Basic Iterative Method for the Implicit Complementarity Problem", journal = "J. Optim. Theory Appl.", volume = "37", pages = "149--162", kwds = "iter, constr" } @article{pasa:77, author = "C. C. Paige and M. A. Saunders", year = "1977", title = "Least Squares Estimation of Discrete Linear Dynamic Systems Using Orthogonal Transformations", journal = "SIAM J. Numer. Anal.", volume = "14", pages = "180--193", kwds = "contr, qrd" } @article{pasa:81, author = "C. C. Paige and M. A. Saunders", year = "1981", title = "Toward a Generalized Singular Value Decomposition", journal = "SIAM J. Numer. Anal.", volume = "18", pages = "398--405", kwds = "gsvd, csd" } @article{pasa:82, author = "C. C. Paige and M. A. Saunders", year = "1982", title = "{LSQR}. {An} Algorithm for Sparse Linear Equations and Sparse Least Squares", journal = "ACM Trans. Math. Software", volume = "8", pages = "43--71", kwds = "iter, cg, lanczos" } @article{pasa:82a, author = "C. C. Paige and M. A. Saunders", year = "1982", title = "Algorithm {\rm 583} {LSQR}: Sparse Linear Equations and Sparse Least Squares", journal = "ACM Trans. Math. Software", volume = "8", pages = "195--209", kwds = "iter, cg, lanczos, soft" } @article{pavd:86, author = "C. C. Paige and P. {Van Dooren}", year = "1986", title = "On the Quadratic Convergence of {Kogbetliantz's} Algorithm for Computing the Singular Value Decomposition", journal = "Linear Algebra Appl.", volume = "77", pages = "301--313", kwds = "svd" } @article{pawe:93, author = "C. C. Paige and M. Wei", year = "1993", title = "Analysis of the Generalized Total Least Squares Problem {$AX\approx B$} when Some Columns are Free of Errors", journal = "Numer. Math.", volume = "65", pages = "177--202", kwds = "err, tls" } @article{pawe:94, author = "C. C. Paige and M. Wei", year = "1994", title = "History and Generality of the {CS} Decomposition", journal = "Linear Algebra Appl.", volume = "108/109", pages = "303--326", kwds = "csd, survey" } @article{pan:90, author = "C. T. Pan", year = "1990", title = "A Modification to the {LINPACK} Downdating Algorithm", journal = "BIT", volume = "30", pages = "707--722", kwds = "upd, sigp, hyp" } @article{pan:93, author = "C. T. Pan", year = "1993", title = "A Perturbation Analysis on the Problem of Downdating a {Cholesky} Factorization", journal = "Linear Algebra Appl.", volume = "183", pages = "103--116", kwds = "upd, pert" } @article{papl:89, author = "C. T. Pan and R. J. Plemmons", year = "1989", title = "Least Squares Modifications with Inverse Factorizations: Parallel Implementations", journal = "J. Comput. Appl. Math.", volume = "27", pages = "109--127", kwds = "upd, prll" } @article{pasp:89, author = "E. P. Papadopoulou and Y. G. Saridakis and T. S. Papatheodorou", year = "1989", title = "Block {AOR} Iterative Schemes for Large-Scale Least-Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "26", pages = "637--660", kwds = "iter" } @techreport{pael:93, author = "H. Park and L. Eld\'en", year = "1993", title = "Fast and Accurate Triangularization of {Toeplitz} Matrices", institution = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", type = "{Tech. Report}", number = "LiTH-MAT-R-1993-17", kwds = "toep, qrd" } @article{pael:95, author = "H. Park and L. Eld\'en", year = "1995", title = "Downdating the Rank-Revealing {URV} Decomposition", journal = "SIAM J. Matrix. Anal. Appl.", volume = "16", pages = "138--155", kwds = "upd, rrqrd" } @article{pavh:95, author = "H. Park and S. {Van Huffel}", year = "1995", title = "Two-Way Bidiagonalization Scheme for Downdating the Singular Value Decomposition", journal = "Linear Algebra Appl.", volume = "222", pages = "23--40", kwds = "upd, svd" } @book{parl:80, author = "B. N. Parlett", year = "1980", title = "The Symmetric Eigenvalue Problem", publisher = "Prentice-Hall", address = "Englewood Cliffs, NJ", kwds = "eig, survey" } @article{pare:70, author = "B. N. Parlett and J. K. Reid", year = "1970", title = "On the Solution of a System of Linear Equations whose Matrix is Symmetric but not Definite", journal = "BIT", volume = "10", pages = "386--397", kwds = "augms" } @article{part:61, author = "S. V. Parter", year = "1961", title = "The Use of Linear Graphs in {Gauss} Elimination", journal = "SIAM Review", volume = "3", pages = "119--130", kwds = "sparse, graph" } @phdthesis{paze:73, author = "P. Pazelt", year = "1973", title = "{Ein Algoritmus zur L{\"o}sung von Ausgleichproblemen mit Ungleichungen als Nebenbedingungen}", school = "University of W{\"u}rtzburg", address = "Germany", type = "Diplomarbeit", kwds = "constr, soft" } @article{penr:55, author = "R. Penrose", year = "1955", title = "A Generalized Inverse for Matrices", journal = "Proc. Cambridge Philos. Soc.", volume = "51", pages = "406--413", kwds = "ginv" } @article{penr:56, author = "R. PENROSE", year = "1956", title = "On Best Approximate Solutions of Linear Matrix Equations", journal = "Proc. Cambridge Philos. Soc.", volume = "52", pages = "17--19", kwds = "ginv" } @article{pere:67, author = "V. Pereyra", year = "1967", title = "Iterative Methods for Solving Nonlinear Least Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "4", pages = "27--36", kwds = "nlsq, ginv" } @article{pewi:70, author = "G. Peters and J. H. Wilkinson", year = "1970", title = "The Least Squares Problem and Pseudo-Inverses", journal = "Comput. J.", volume = "13", pages = "309--316", kwds = "lud, ne, rank" } @techreport{pile:95, author = "D. J. Pierce and J. G. Lewis", year = "1995", title = "Sparse Multifrontal Rank Revealing {QR} Factorization", institution = "Boeing Information and Support Services", address = "Seattle, WA", type = "{Tech. Report}", number = "MEA-TR-193-Revised", kwds = "sparse, qrd" } pl- @article{plac:72, author = "R. L. Placket", year ="1972", title = "The Discovery of the Method of Least Squares", journal = "Biometrika", volume = "59", pages = "239--251", kwds = "hist" } @article{plem:72, author = "R. J. Plemmons", year = "1972", title = "Monotonicity and Iterative Approximations Involving Rectangular Matrices", journal = "Math. Comp.", volume = "26", pages = "853--858", kwds = "iter" } @article{plem:74, author = "R. J. Plemmons", year = "1974", title = "Linear Least Squares by Elimination and {MGS}", journal = "J. Assoc. Comput. Mach.", volume = "21", pages = "581--585", kwds = "grsch, lud" } @inproceedings{plem:79, author = "R. J. Plemmons", year = "1979", title = "Adjustment by Least Squares in Geodesy using Block Iterative Methods for Sparse Matrices", booktitle = "Proceedings of the 1979 Army Numerical Analysis and Computer Conference", pages = "151--186", address = "El Paso, TX", kwds = "iter, geod" } @techreport{plem:92, author = "R. J. Plemmons", year = "1992", title = "A Proposal for {FFT} Based Fast Recursive Least Squares", institution = "Institute for Mathematics and Its Applications, University of Minnesota", address = "Minneapolis, MN", type = "{Tech. Report}", number = "\#982", kwds = "toep, rls" } po- @article{pojv:94, author = "L.F. PORTUGAL and J.J. J\'UDICE and L.N. VICENTE", year = "1994", title = "A Comparison of Block Pivoting and Interior-Point Algorithms for Linear Least Squares Problems with Nonnegative Variables", journal = "Math. Comp.", volume = "63", pages = "625--643", kwds = "sparse, constr" } @phdthesis{poth:84, author = "A. Pothen", year = "1984", title = "Sparse Null Bases and Marriage Theorems", school = "Cornell University", address = "Ithaca, NY", type = "{Ph. D.} thesis", kwds = "sparse, graph" } @article{poth:93, author = "A. Pothen", year = "1993", title = "Predicting the Structure of Sparse Orthogonal Factors", journal = "Linear Algebra Appl.", volume = "194", pages = "183--204", kwds = "sparse, house" } @article{pofa:90, author = "A. Pothen and C. -J. Fan", year = "1990", title = "Computing the Block Triangular Form of a Sparse Matrix", journal = "ACM Trans. Math. Software", volume = "16", pages = "303--324", kwds = "perm, sparse" } @article{pora:89, author = "A. Pothen and P. Raghavan", year = "1989", title = "Distributed Orthogonal Factorization: {Givens} and {Householder} Algorithms", journal = "SIAM J. Sci. Statist. Comput.", volume = "10", pages = "1113--1134", kwds = "qrd, prll, house, rot" } @inproceedings{pore:69, author = "M. J. D. Powell and J. K. Reid", year = "1969", title = "On Applying {Householder's} Method to Linear Least Squares Problems", booktitle = "Proceedings of the IFIP Congress 68", editor = "A. J. M. Morell", pages = "122--126", publisher = "North-Holland, Amsterdam", address = "", kwds = "wlsq, house" } @article{prat:87, author = "V. Pratt", year = "1987", title = "Direct Least Squares Fitting of Algebraic Surfaces", journal = "ACM J. Comput. Graphics", volume = "21:4", pages = "", kwds = "nlsq, geom" } pu- @phdthesis{pugl:93, author = "C. Puglisi", year = "1993", title = "{QR} Factorization of Large Sparse Overdetermined and Square Matrices with the Multifrontal Method in a Multiprocessing Environment", school = "Institut National Polytechnique de Toulouse", institution = "CERFACS", address = "Toulouse, France", type = "{Ph. D.} thesis", kwds = "sparse, thesis" } ra- re- @article{rawe:77, author = "H. Ramsin and P.-{\AA}. Wedin", year = "1977", title = "A Comparison of Some Algorithms for the Nonlinear Least Squares Problem", journal = "BIT", volume = "17", pages = "72--90", kwds = "nlsq, test" } @article{rast:88, author = "C. M. Rader and A. O. Steinhardt", year = "1988", title = "Hyperbolic {Householder} transforms", journal = "SIAM J. Matrix Anal. Appl.", volume = "9", pages = "269--290", kwds = "downd, hyp" } @book{rao:73, author = "R. C. Rao", year = "1973", title = "Linear Statistical Inference and Its Applications, {\rm 2nd ed.}", publisher = "John Wiley", address = "New York", kwds = "stat, survey" } %re- @article{reic:91, author = "L. Reichel", year = "1991", title = "Fast {QR} Decomposition of {Vandermonde}-like Matrices and Polynomial Least Squares Approximation", journal = "SIAM J. Matrix Anal. Appl.", volume = "12", pages = "552--564", kwds = "poly, vand" } @article{regr:90, author = "L. Reichel and W. B. Gragg", year = "1990", title = "{FORTRAN} subroutines for updating the {QR} decomposition", journal = "ACM Trans. Math. Software", volume = "16", pages = "369--377", kwds = "upd, downd, soft, qrd, grsch" } @article{reag:91, author = "L. Reichel and G. S. Ammar and W. B. Gragg", year = "1991", title = "Discrete Least Squares Approximation by Trigonometric Polynomials", journal = "Math. Comp.", volume = "57", pages = "273--289", kwds = "poly" } @article{reid:67, author = "J. K. Reid", year = "1967", title = "A Note on the Least Squares Solution of a Band System of Linear Equations by {Householder} Reductions", journal = "Comput J.", volume = "10", pages = "188--189", kwds = "band, house, qrd" } @inproceedings{reid:71, author = "J. K. Reid", year = "1971", title = "On the Method of Conjugate Gradients for the Solution of Large Systems of Linear Equations", pages = "231--254", booktitle = "Large Sparse Sets of Linear Equations", editor = "J.~K. Reid", publisher = "Academic Press, New York", kwds = "sparse, iter, cg" } @article{reid:72, author = "J. K. Reid", year = "1972", title = "On the Use of Conjugate Gradients for Systems of Linear Equations Possessing {``Property A''}", journal = "SIAM J. Numer. Anal.", volume = "9", pages = "325--332", kwds = "iter, cg" } @techreport{reid:84, author = "J. K. Reid ", year = "1984", title = "{TREESOLVE}, a {Fortran} Package for Solving Large Sets of Linear Finite Element Solutions", institution = " Computer Science and Systems Division, AERE Harwell", address = "Oxfordshire, UK", type = "{Tech. Report}", number = "CSS 155, 1984", kwds = "sparse, multfr" } @inproceedings{reid:87, author = "J. K. Reid ", year = "1987", title = "Sparse Matrices", booktitle = "The State of the Art in Numerical Analysis", editor = "A. Iserles and M. J. D. Powell", pages = "59--86", publisher = "Oxford University Press, London, UK", kwds = "sparse" } @article{rein:71, author = "C. H. Reinsch", year = "1971", title = "Smoothing by Spline Functions", journal = "Numer. Math.", volume = "16", pages = "451--454.", kwds = "spline, regul" } %ri- @article{rice:66, author = "J. R. Rice", year = "1966", title = "Experiments on {Gram-Schmidt} orthogonalization", journal = "Math. Comp.", volume = "20", pages = "325--328", kwds = "grsch, err" } @techreport{rice:83, author = "J. R. Rice", year = "1983", title = "{PARVEC} Workshop on Very Large Least Squares Problems and Supercomputers", institution = "Purdue University", address = "West Lafayette, IN", type = "{Tech. Report}", number = "CSD-TR 464", kwds = "sparse, survey" } @article{riga:67, author = "J. L. Rigal and J. Gaches", year = "1967", title = "On the Compatability of a Given Solution with the Data of a Linear System", journal = "J. Assoc. Comput. Mach.", volume = "14", pages = "543--548", kwds = "err" } @article{rile:56, author = "J. D. Riley", year = "1956", title = "Solving Systems of Linear Equations with a Positive Definite Symmetric but Possibly Ill-Conditioned Matrix", journal = "Math. Tables Aids. Comput.", volume = "9", pages = "96--101", kwds = "regul" } %ru- @inproceedings{rose:72, author = "D. J. Rose", year = "1972", title = "A Graph-Theoretic Study of the Numerical Solution of Sparse Positive Definite Systems of Linear Equations", booktitle = "Graph Theory and Computing", editor = "R. C. Read", pages = "183--217", publisher = "Academic Press, New York", kwds = "sparse, graph" } @article{ruhe:79, author = "A. Ruhe", year = "1979", title = "Accelerated {Gauss-Newton} Algorithms for Nonlinear Least Squares Problems", journal = "BIT", volume = "19", pages = "356--367", kwds = "nlsq" } @article{ruhe:83, author = "A. Ruhe", year = "1983", title = "Numerical Aspects of {Gram-Schmidt} Orthogonalization of Vectors", journal = "Linear Algebra Appl.", volume = "52/53", pages = "591--601", kwds = "grsch, orth" } @article{ruwe:80, author = "A. Ruhe and P.-{\AA}. Wedin", year = "1980", title = "Algorithms for Separable Nonlinear Least Squares Problems", journal = "SIAM Review", volume = "22", pages = "318--337", kwds = "varpro, nlsq" } rut- @article{ruti:54, author = "H. Rutishauser", year = "1954", title = "Der {Quotienten-Differenzen-Algorithmus}", journal = "ZAMP", volume = "5", pages = "233--251", kwds = "svd" } @incollection{ruti:59, author = "H. Rutishauser", title = "Theory of Gradient Methods", year = "1959", booktitle = "Refined Methods for Computation of the Solution and the Eigenvalues of Self-Adjoint Boundary Value Problems", editor = "M. Engeli and Th. Ginsburg and H. Rutishauser and E. Stiefel", publisher = "Birkh{\"a}user", address = "Basel/Stuttgart", pages = "24--50", kwds = "nlsq, opt" } @book{ruti:67, author = "H. Rutishauser", year = "1967", title = "Description of {Algol} {\rm 60}", series = "Handbook for Automatic Computation, Vol. 1a", publisher = "Springer-Verlag", address = "Berlin", kwds = "prog" } @article{ruti:68, author = "H. Rutishauser", year = "1968", title = "Once Again: The Least Squares Problem", journal = "Linear Algebra Appl.", volume = "1", pages = "479--488", kwds = "regul" } @book{ruti:76, author = "H. Rutishauser", year = "1976", title = "{Vorlesungen {\"u}ber Numerische Mathematik}. Band {\rm 1}", publisher = "Birkh{\"a}user", address = "Basel", kwds = "nla, survey" } sa- @article{saad:80, author = "Y. Saad", year = "1980", title = "On the Rates of Convergence of the {Lanczos} and Block-{Lanczos} Methods", journal = "SIAM J. Numer. Anal.", volume = "17", pages = "687--706", kwds = "iter, lanczos" } @article{saad:88, author = "Y. Saad", year = "1988", title = "Preconditioning Techniques for Nonsymmetric and Indefinite Linear Systems", journal = "J. Comput. Appl. Math.", volume = "24", pages = "89--105", kwds = "precond" } @book{saad:92, author = "Y. Saad", year = "1992", title = "Numerical Methods for Large Eigenvalue Problems", publisher = "Manchester University Press", address = "Manchester, UK", kwds = "iter" } @article{sala:87, author = "D. E. Salane", year = "1987", title = "A Continuation Approach for Solving Large Residual Least Squares Problems", journal = "SIAM J. Sci. Statist. Comput.", volume = "8", pages = "655--671", kwds = "nlsq" } @techreport{saun:72, author = "M. A. Saunders", year = "1972", title = "Large-Scale Linear Programming Using The {Cholesky} Factorization", institution = "Computer Science Department, Stanford University", address = "CA", type = "{Tech. Report}", number = "CS252", kwds = "chol, upd, downd" } @inproceedings{saun:79, author = "M. A. Saunders", year = "1979", title = "Sparse Least Squares by Conjugate Gradients: {A} Comparison of Preconditioning Methods", booktitle = "Proceedings of Computer Science and Statistics: Twelfth Annual Conference on the Interface", editor = "", pages = "", publisher = "", address = "Waterloo, Canada", kwds = "iter, precond, cg" } @article{saun:95, author = "M. A. Saunders", year = "1995", title = "Solution of Sparse Rectangular Systems Using {LSQR} and {CRAIG}", journal = "BIT", volume = "35", pages = "588--604", kwds = "iter, cg, lanczos" } @article{saut:78, author = "W. Sautter", year = "1978", title = "{F}ehleranalyse f{\"u}r die {G}auss-{E}limination zur {B}erechnung der {L}{\"o}sung minimaler {L}{\"a}nge", journal = "Numer. Math.", volume = "30", pages = "165--184", kwds = "rank, ginv" } sc- @article{scha:85, author = "R. Schaback", year = "1985", title = "Convergence Analysis of the General {Gauss-Newton} Algorithm", journal = "Numer. Math.", volume = "46", pages = "281--309", kwds = "nlsq" } @article{schi:83, author = "K. Schittkowski", year = "1983", title = "The Numerical Solution of Constrained Linear Least-squares Problems", journal = "IMA J. Numer. Anal.", volume = "3", pages = "11--36", kwds = "constr" } @incollection{schi:85, author = "K. Schittkowski", year = "1985", title = "Solving Constrained Nonlinear Least Squares Problems by a General Purpose {SOP}-method", booktitle = "Trends in Mathematical Optimization", editor = "K.-H. Hoffmann and J. -B. Hiriart-Urruty and C. Lemar\'echal and J. Zowe", series = "International Series of Numerical Mathematics", volume = "84", publisher = "Birkh{\"a}user-Verlag, Basel, Switzerland", pages = "49--83", kwds = "nlsq" } @article{scst:79, author = "K. Schittkowski and J. Stoer", year = "1979", title = "A Factorization Method for the Solution of Constrained Linear Least Squares Problems Allowing Subsequent Data Changes", journal = "Numer. Math.", volume = "31", pages = "431--463", kwds = "qrd, constr, upd, grsch" } @techreport{sczi:85, author = "K. Schittkowski and P. Zimmermann", year = "1985", title = "A Factorization Method for Constrained Least Squares Problems with Data Changes. {Part} {\rm 2}: Numerical Tests, Comparisons, and {ALGOL} Codes", institution = "Institut f{\"u}r Angewandte Mathematik und Statistik, Universit{\"a}t W{\"u}rzburg", address = "Germany", type = "{Tech. Report}", number = "Preprint No. 30", kwds = "qrd, constr, upd, soft, grsch" } @article{schm:07, author = "E. Schmidt", year = "1907", title = "{Zur Theorie der linearen und nichtlinearen Integralgleichungen. I. Teil: Entwicklung willk\"urlicher Funktionen nach System vorgeschriebener}", journal = "Math. Ann.", volume = "63", pages = "433--476", kwds = "grsch" } @article{schm:08, author = "E. Schmidt", year = "1908", title = "{\"U}ber die {A}ufl{\"o}sung linearer {G}leichungen mit unendlich vielen {U}nbekannten", journal = "Rend. Circ. Mat. Palermo. Ser. 1", volume = "25", pages = "53--77", kwds = "grsch" } @article{scta:86, author = "R. Schreiber and W.-P. Tang", year = "1986", title = "On Systolic Arrays for Updating the {Cholesky} Factorization", journal = "BIT", volume = "26", pages = "451--466", kwds = "chol,syst,upd,downd" } @article{scvl:89, author = "R. Schreiber and C. F. {Van Loan}", year = "1989", title = "A Storage Efficient {WY} Representation for Products of {Householder} Transformations", journal = "SIAM J. Sci. Statist. Comput.", volume = "10", pages = "53--57", kwds = "block, prll, house" } @article{scti:85, author = "H. Schwetlick and V. Tiller", year = "1985", title = "Numerical Methods for Estimating Parameters in Nonlinear Models with Errors in the Variables", journal = "Technometrics", volume = "27", pages = "17--24", kwds = "nlsq, tls, orthreg" } @inproceedings{scol:72, author = "H. D. Scolnik", year = "1972", title = "On the Solution of Non-linear Least Squares Problems", booktitle = "Proceedings of the {IFIP} Congress 71", editor = "H. Freeman", pages = "1258--1265", publisher = "North-Holland, Amsterdam", kwds = "varpro, nlsq" } @book{sebe:77, author = "G. A. F. Seber", year = "1977", title = "Linear Regression Analysis", publisher = "John Wiley", address = "New York", kwds = "regr, stat, survey" } @article{seid:1874, author = "P. L. Seidel", year = "1874", title = "{\"U}ber ein {V}erfahren, die {G}leichungen, auf welche die {M}ethode der kleinsten {Q}uadrate f{\"u}hrt, sowie lineare {G}leichungen {\"u}berhaupt, durch successive {A}nn{\"a}herung aufzul{\"o}sen", journal = "Abh. Bayer Akad. Wiss.", volume = "11:81", pages = "", kwds = "iter" } @article{sham:75, author = "L. F. Shampine", year = "1975", title = "Discrete Least Squares Polynomial Fits", journal = "Comm. ACM", volume = "18", pages = "179--180", kwds = "scale, lud" } @article{sher:78, author = "A. H. Sherman", year = "1978", title = "Algorithm {\rm 533}, {NSPIV}, a {FORTRAN} Subroutine for Sparse {Gaussian} Elimination with Partial Pivoting", journal = "ACM Trans. Math. Software", volume = "4", pages = "391--398", kwds = "sparse, lud" } @article{sieg:65, author = "I. H. Siegel", year = "1965", title = "Deferment of Computation in the Method of Least Squares", journal = "Math. Comp.", volume = "19", pages = "329--331", kwds = "augms" } sk- @article{skee:79, author = "R. D. Skeel", year = "1979", title = "Scaling for Numerical Stability in {Gaussian} Elimination", journal = "J. Assoc. Comput. Mach.", volume = "26", pages = "494--526", kwds = "scale, lud" } @article{skee:80, author = "R. D. Skeel", year = "1980", title = "Iterative Refinement Implies Numerical Stability for {Gaussian} Elimination", journal = "Math. Comp.", volume = "35", pages = "817--832", kwds = "ir, lud" } sl- @article{slui:69, author = "A. van der Sluis", year = "1969", title = "Condition Numbers and Equilibration of Matrices", journal = "Numer. Math.", volume = "14", pages = "14--23", kwds = "pert, cond, scale" } @article{slui:75, author = "A. van der Sluis", year = "1975", title = "Stability of the Solutions of Linear Least Squares Problems", journal = "Numer. Math.", volume = "23", pages = "241--254", kwds = "err, pert" } @article{slve:79, author = "A. van der Sluis and G. Veltkamp", year = "1979", title = "Restoring Rank and Consistency by Orthogonal Projection", journal = "Linear Algebra Appl.", volume = "28", pages = "257--278", kwds = "rank, orth" } @incollection{slvo:87, author = "A. van der Sluis and H. van der Vorst", year = "1987", title = "Numerical Solution of Large Sparse Linear Equations and Least Squares Problems", booktitle = "Seismic Tomography", editor = "G. Nolet", publisher = "Reidel, Dordrecht, the Netherlands", pages = "49--83", kwds = "rank, orth" } @article{slvo:90, author = "A. van der Sluis and H. van der Vorst", year = "1990", title = "{SIRT-} and {CG-}Type Methods for Iterative Solution of Sparse Linear Least-Squares Problems", journal = "Linear Algebra Appl.", volume = "130", pages = "257--302", kwds = "iter, cg" } @phdthesis{sode:93, author = "I. S{\"o}derquist", year = "1993", title = "Computing Parameters in Nonlinear Least Squares Models", school = "University of Ume{\aa}", institution = "Department of Computer Science", address = "Sweden", type = "{Ph. D.} thesis", kwds = "nlsq, constr" } %st- @article{spat:82, author = "H. Sp{\"a}th", year = "1982", title = "On Discrete Linear Orthogonal $L_p$ Approximation", journal = "Z. Angew. Math. Mech.", volume = "62", pages = "354--355", kwds = "nlsq, geom" } @article{spat:86, author = "H. Sp{\"a}th", year = "1986", title = "Orthogonal Least Squares Fitting with Linear Manifolds", journal = "Numer. Math.", volume = "48", pages = "441--445", kwds = "nlsq, geom" } @article{spat:90, author = "H. Sp{\"a}th", year = "1990", title = "Modified {Gram-Schmid}t for Solving Linear Least Squares Problems is Equivalent to {Gaussian} Elimination for the Normal Equations", journal = "Appl. Math.", volume = "20", pages = "587--589", kwds = "ne, grsch" } @book{spat:92, author = "H. Sp{\"a}th", year = "1992", title = "Mathematical Algorithms for Linear Regression", publisher = "Academic Press", address = "New York", kwds = "regr, stat, survey" } @article{stew:69, author = "G.W. STEWART", year = "1969", title = "On the Continuity of the Generalized Inverse", journal = "SIAM J. Appl. Math.", volume = "17", pages = "33--45", kwds = "nla, pert, ginv" } @book{stew:73, author = "G.W. STEWART", year = "1973", title = "Introduction to Matrix Computations", publisher = "Academic Press", address = "New York", kwds = "nla, survey" } @article{stew:76, author = "G.W. STEWART", year = "1976", title = "The Economical Storage of Plane Rotations", journal = "Numer. Math.", volume = "25", pages = "137--138.", kwds = "qrd, rot" } @article{stew:77, author = "G.W. STEWART", year = "1977", title = "Perturbation Bounds for the {QR} Factorization of a Matrix", journal = "SIAM J. Numer. Anal.", volume = "14", pages = "509--518", kwds = "err, qrd" } @inproceedings{stew:77a, author = "G.W. STEWART", year = "1977", title = "Research Development and {LINPACK}", booktitle = "Mathematical Software III", editor = "J. R. Rice", publisher = "Academic Press, New York", pages = "1-14", kwds = "soft, pert, survey" } @article{stew:77b, author = "G.W. STEWART", year = "1977", title = "On the Perturbation of Pseudo-Inverses, Projections, and Linear Least Squares Problems", journal = "SIAM Review", volume = "19", pages = "634-662", kwds = "nla, pert, ginv, orth" } @article{stew:79, author = "G.W. STEWART", year = "1979", title = "The Effects of Rounding Error on an Algorithm for Downdating a {Cholesky} Factorization", journal = "J. Inst. Maths. Applic.", volume = "23", pages = "203-213", kwds = "nla, err, downd, chol" } @article{stew:79a, author = "G.W. STEWART", year = "1979", title = "A Note on the Perturbation of Singular Values", journal = "Linear Algebra Appl.", volume = "28", pages = "213--216", kwds = "svd, pert" } @article{stew:80, author = "G.W. STEWART", year = "1980", title = "The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators", journal = "SIAM J. Numer. Anal.", volume = "17", pages = "403--404", kwds = "nla, rand, qrd, cond, orth" } @article{stew:81, author = "G.W. STEWART", year = "1981", title = "On the Implicit Deflation of Nearly Singular Systems of Linear Equations", journal = "SIAM J. Sci. Statist. Comput.", volume = "2", pages = "136--140", kwds = "rank,ginv" } @article{stew:82, author = "G.W. STEWART", year = "1982", title = "Computing the {CS} Decomposition of a Partitioned Orthogonal Matrix", journal = "Numer. Math.", volume = "40", pages = "297-306", kwds = "svd, csd, orth" } @inproceedings{stew:83, author = "G.W. STEWART", year = "1983", title = "A Method for Computing the Generalized Singular Value Decomposition", pages = "207--220", booktitle = "Matrix Pencils. Proceedings, Pite Havsbad, 1982", editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", publisher = "Springer-Verlag, Berlin", series = "Lecture Notes in Mathematics", volume = "973", kwds = "gsvd" } @techreport{stew:83a, author = "G.W. STEWART", year = "1983", title = "A Generalization of the {Eckart-Young} Approximation Theorem", institution = "Department of Computer Science, University of Maryland", address = "College Park, MD", number = "TR-1325", kwds = "pert, max, tls" } @techreport{stew:83b, author = "G.W. STEWART", year = "1983", title = "A Nonlinear Version of {Gauss's} Minimum Variance Theorem with Applications to an Errors-in-the-Variables Model", institution = "Department of Computer Science, University of Maryland", address = "College Park, MD", type = "{Tech. Report}", number = "TR-1263", kwds = "tls, regr, nlsq, pert" } @article{stew:84, author = "G.W. STEWART", year = "1984", title = "Rank Degeneracy", journal = "SIAM J. Sci. Statist. Comput.", volume = "5", pages = "403--413", kwds = "rank, rrqrd" } @article{stew:84a, author = "G.W. STEWART", year = "1984", title = "On the Invariance of Perturbed Null Vectors under Column Scaling", journal = "Numer. Math.", volume = "44", pages = "61--65", kwds = "scale, pert" } @article{stew:84b, author = "G.W. STEWART", year = "1984", title = "On the Asymptotic Behavior of Scaled Singular and {QR} Decompositions", journal = "Math. Comp.", volume = "43(168)", pages = "168--489", kwds = "rank, rrqrd" } @article{stew:87, author = "G.W. STEWART", year = "1987", title = "Collinearity and Least Squares Regression", journal = "Statistical Science", volume = "2", pages = "68-100", kwds = "stat, regr, tls, rank" } @article{stew:90, author = "G.W. STEWART", year = "1990", title = "On Scaled Projections and Pseudoinverses", journal = "Linear Algebra Appl.", volume = "132", pages = "115--117", kwds = "wlsq" } @inproceedings{stew:90a, author = "G.W. STEWART", year = "1990", title = "Perturbation Theory and Least Squares with Errors in the Variables", booktitle = "Contemporary Mathematics 112: Statistical Analysis of Measurement Error Models and Applications", editor = "P. J. Brown and W. A. Fuller", pages = "171--181", publisher = "American Mathematical Society, Providence, RI", kwds = "stat, pert, regr" } @techreport{stew:91, author = "G.W. STEWART", year = "1991", title = "On an Algorithm for Refining a Rank-Revealing {URV} Factorization and a Perturbation Theorem for Singular Values", institution = "Department of Computer Science, University of Maryland", address = "College Park, MD", type = "{Tech. Report}", number = "UMIACS-TR-91-38, CS-TR-2626", kwds = "rrqrd, pert, svd" } @article{stew:92, author = "G.W. STEWART", year = "1992", title = "An Updating Algorithm for Subspace Tracking", journal = "IEEE Trans. Signal Processing", volume = "40", pages = "1535--1541", kwds = "upd, rrqrd" } @article{stew:93a, author = "G.W. STEWART", year = "1993", title = "Updating a Rank-Revealing {ULV} Decomposition", journal = "SIAM J. Matrix Anal. Appl.", volume = "14", pages = "494--499", kwds = "upd, rrqrd" } @article{stew:93b, author = "G.W. STEWART", year = "1993", title = "On the Perturbation of {LU}, {Cholesky}, and {QR} Factorizations", journal = "SIAM J. Matrix Anal. Appl.", volume = "14", pages = "1141--1145", kwds = "pert, qrd, chol" } @article{stew:93c, author = "G.W. STEWART", year = "1993", title = "On the Early History of the Singular Value Decomposition", journal = "SIAM Review", volume = "35", pages = "551--566", kwds = "svd, hist" } @techreport{stew:94, author = "G.W. STEWART", year = "1994", title = "On the Stability of Sequential Updates and Downdates", institution = "Department of Computer Science, University of Maryland", address = "College Park, MD", type = "{Tech. Report}", number = "CS-TR-3238", kwds = "downd, stab" } @book{stsu:90, author = "G.W. STEWART and J.{-G}. SUN", year = "1990", title = "Matrix Perturbation Theory", publisher = "Academic Press", address = "Boston", kwds = "pert, survey" } @article{stie:52, author = "E. Stiefel", year = "1952/53", title = "{Ausgleichung ohne Aufstellung der Gausschen Normalgleichungen}", journal = "Wiss. Z. Tech. Hochsch. Dresden", volume = "2", pages = "441--442", kwds = "cg, iter" } @article{stie:77, author = "S. M. Stigler", year = "1977", title = "An Attack on {Gauss}, Published by {Legendre} in {\rm 1820}", journal = "Hist. Math.", volume = "4", pages = "31--35", kwds = "hist" } @article{stie:81, author = "S. M. Stigler", year = "1981", title = "{Gauss} and the Invention of Least Squares", journal = "Ann. Statist.", volume = "9", pages = "465--474", kwds = "hist" } @article{stie:1887, author = "T. J. Stieltjes", year = "1887", title = "Sur les racines de l'{\'e}quation $x_n=0$", journal = "Acta. Math.", volume = "9", pages = "385--400", kwds = "iter" } @article{stoe:71, author = "J. Stoer", year = "1971", title = "On the Numerical Solution of Constrained Least Squares Problems", journal = "SIAM J. Numer. Anal.", volume = "8", pages = "382--411", kwds = "constr, upd" } @article{stra:91, author = "Z. Strakos", year = "1991", title = "On the Real Convergence of the Conjugate Gradient Method", journal = "Linear Algebra Appl.", volume = "154/156", pages = "535--549", kwds = "cg, lanczos, iter" } @article{stra:74, author = "C. N. Strand", year = "1974", title = "Theory and Methods Related to the Singular Function Expansion and {Landweber's} Iteration for Integral Equations of the First Kind", journal = "SIAM J. Numer. Anal.", volume = "11", pages = "798--825", kwds = "iter, regul" } %su- @techreport{sunc:95, author = "C. Sun", year = "1995", title = "Parallel Solution of Sparse Linear Least Squares Problems on Distributed-Memory Multiprocessors", institution = "Advanced Computing Research Institute, Cornell University", address = "Ithaca, NY", type = "{Tech. Report}", number = "CTC95TR212, 05/95", kwds = "sparse, qrd, prll" } @article{sunc:96, author = "C. Sun", year = "1996", title = "Parallel Sparse Orthogonal Factorization on Distributed-Memory Multiprocessors", journal = "SIAM J. Sci. Comput.", note = "to appear", volume = "", pages = "", kwds = "sparse, qrd, prll" } @article{sun:91, author = "J.-G. Sun", year = "1991", title = "Perturbation Bounds for the {Cholesky} and {QR} Factorizations", journal = "BIT", volume = "31", pages = "341--352", kwds = "pert, chol, qrd" } @article{sun:95a, author = "J.-G. Sun", year = "1995", title = "Perturbation Analysis of the {Cholesky} Downdating and {QR} Updating Problems", journal = "SIAM J. Matrix Anal. Appl.", volume = "16", pages = "760--775", kwds = "err, pert, upd", } @article{sun:96, author = "J.-G. Sun", year = "1996", title = "Optimal Backward Perturbation Bounds for the Linear {LS} Problem With Multiple Right-Hand Sides", journal = "IMA J. Numer. Anal.", volume = "16", pages = "1--11", kwds = "err, pert", } %sw- @article{swee:84, author = "D. R. Sweet", year = "1984", title = "Fast {Toeplitz} Orthogonalization", journal = "Numer. Math.", volume = "43", pages = "1--21", kwds = "qrd, toep" } @article{swee:91, author = "D. R. Sweet", year = "1991", title = "Fast Block {Toeplitz} Orthogonalization", journal = "Numer. Math.", volume = "58", pages = "613--629", kwds = "qrd, toep" } %ta- @article{tana:71, author = "K. Tanabe", year = "1971", title = "Projection Method for Solving a Singular System of Linear Equations and its Applications", journal = "Numer. Math.", volume = "17", pages = "203--214", kwds = "iter, ginv" } @article{tang:94, author = "P. T. P. Tang", year = "1994", title = "Dynamic Condition Estimation and {Rayleigh-Ritz} Approximation", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "331--346", kwds = "cond" } @article{tago:81, author = "W.-P. Tang and G. H. Golub", year = "1987", title = "The Block Decomposition of a {Vandermonde} Matrix and Its Applications", journal = "BIT", volume = "21", pages = "505--517", kwds = "block, vand" } @article{tarj:72, author = "R. E. Tarjan", year = "1972", title = "Depth-first Search and Linear Graph Algorithms", journal = "SIAM J. Comput.", volume = "1", pages = "146--159", kwds = "sparse, graph" } @article{tewa:68, author = "R. P. Tewarson", year = "1968", title = "A Computational Method for Evaluating Generalized Inverses", journal = "Comput. J.", volume = "10", pages = "411--413", kwds = "ginv" } @article{tiho:63, author = "A.N. TIKHONOV", year = "1963", title = "Regularization of Incorrectly Posed Problems", journal = "Soviet Math.", volume = "4", pages = "1624--1627", kwds = "regul, survey" } @article{tiwa:67, author = "W. F. Tinney and J. W. Walker", year = "1967", title = "Direct Solution of Sparse Network Equations by Optimally Ordered Triangular Factorization", journal = "Proc. IEEE", volume = "55", pages = "1801--1809", kwds = "sparse" } @article{vest:91, author = "N. Vempati and I. W. Slutsker and W. F. Tinney", year = "1991", title = "Enhancements to {Givens} Rotations for Power System State Estimation", journal = "IEEE Trans. Power Systems", volume = "6", pages = "842--849", kwds = "sparse" } @article{tsao:75, author = "N.-K. Tsao", year = "1975", title = "A Note on Implementing the {Householder} Transformation", journal = "SIAM J. Numer. Anal.", volume = "12", pages = "53--58", kwds = "house" } @article{toin:87, author = "P. L. Toint", year = "1987", title = "On Large Scale Nonlinear Least Squares Calculations", journal = "SIAM J. Sci. Statist. Comput.", volume = "8", pages = "416--435", kwds = "sparse, nlsq" } @techreport{toin:87a, author = "P. L. Toint", year = "1987", title = "{VE{\rm 10}AD} A routine for Large-Scale Nonlinear Least Squares", type = "{Harwell} Subroutine Library", institution = "AERE Harwell", address = "Oxfordshire, UK", kwds = "sparse, nlsq, soft" } @techreport{vhjs:76, author = "J. {Van Heijst} and J. Jacobs and J. Scherders", year = "1976", title = "Kleinste-{Kvadraten} {Problemen}.", institution = "Department of Mathematics, Eindhoven University of Technology", address = "Eindhoven, the Netherlands", type = "{Tech. Report}", kwds = "iter, svd" } @phdthesis{vhuf:87, author = "S. {Van Huffel}", year = "1987", title = "Analysis of the Total Least Squares Problem and Its Use in Parameter Estimation", school = "Katholieke Universiteit Leuven, Belgium", institution = "ESAT Lab., Department of Electr. Eng.", type = "{Ph. D.} thesis", kwds = "tls, regr, thesis" } @article{vhuf:91, author = "S. {Van Huffel}", year = "1991", title = "Iterative Algorithms for Computing the Singular Subspace of a Matrix Associated with its Smallest Singular Values", journal = "Linear Algebra Appl.", volume = "154/156", pages = "675--709", kwds = "tls, iter" } @article{vhpa:95, author = "S. {Van Huffel} and H. Park", year = "1995", title = "Efficient Reduction Algorithms for Bordered Band Matrices", journal = "Numer. Linear Algebra Appl.", volume = "2", pages = "95--113", kwds = "upd, svd" } @article{vhva:87, author = "S. {Van Huffel} and J. Vandewalle", year = "1987", title = "Algebraic Relationships Between Classical Regression and Total Least-squares Estimation", journal = "Linear Algebra Appl.", volume = "93", pages = "149--162", kwds = "tls" } @article{vhva:88a, author = "S. {Van Huffel} and J. Vandewalle", year = "1988", title = "Analysis and Solution of the Nongeneric Total Least Squares Problem", journal = "SIAM J. Matrix Anal. Appl.", volume = "9", pages = "360--372", kwds = "tls" } @article{vhva:89, author = "S. {Van Huffel} and J. Vandewalle", year = "1989", title = "Analysis and Properties of the Generalized Total Least Squares Problem {$AX \approx B$} when Some or all Columns in {$A$} are Subject to Error", journal = "SIAM J. Matrix. Anal. Appl.", volume = "10", pages = "294--315", kwds = "tls" } @book{vhva:91, author = "S. {Van Huffel} and J. Vandewalle", year = "1991", title = "The Total Least Squares Problem: Computational Aspects and Analysis", publisher = "SIAM", series = "Frontiers in Applied Mathematics", volume = "9", address = "Philadelphia", kwds = "tls, survey" } @article{vhvh:87, author = "S. {Van Huffel} and J. Vandewalle and A. Haegemans", year = "1987", title = "An Efficient and Reliable Algorithm for Computing the Singular Subspace of a Matrix, Associated with its Smallest Singular Values", journal = "J. Comp. Appl. Math.", volume = "19", pages = "313--330", kwds = "tls, svd" } @article{vhzh:91, author = "S. {Van Huffel} and H. Zha", year = "1991", title = "The Restricted Total Least Squares Problem: Formulation, Algorithm, and Properties", journal = "SIAM J. Matrix Anal. Appl.", volume = "12", pages = "292--309", kwds = "tls, svd" } @article{vhzh:93, author = "S. {Van Huffel} and H. Zha", year = "1993", title = "An Efficient Total Least Squares Algorithm Based on a Rank Revealing Two-sided Orthogonal Decomposition", journal = "Numer. Algorithms", volume = "4", pages = "101--133", kwds = "tls, svd" } @article{vanl:76, author = "C. F. {Van Loan}", year = "1976", title = "Generalizing the Singular Value Decomposition", journal = "SIAM J. Numer. Anal.", volume = "13", pages = "76--83", kwds = "gsvd" } @inproceedings{vanl:83, author = "C. F. {Van Loan}", year = "1983", title = "A Generalized {SVD} Analysis of Some Weighting Methods for Equality Constrained Least Squares", pages = "245--262", booktitle = "Matrix Pencils. Proceedings, Pite Havsbad, 1982", editor = "B. K{\aa}gstr{\"o}m and A. Ruhe", publisher = "Springer-Verlag, Berlin", series = "Lecture Notes in Mathematics", volume = "973", kwds = "constr, wlsq" } @article{vanl:85, author = "C. F. {Van Loan}", year = "1985", title = "Computing the {CS} and the Generalized Singular Value Decomposition", journal = "Numer. Math.", volume = "46", pages = "479--492", kwds = "csd, gsvd" } @article{vanl:85a, author = "C. F. {Van Loan}", year = "1985", title = "On the Method of Weighting for Equality Constrained Least Squares", journal = "SIAM J. Numer. Anal.", volume = "22", pages = "851--864", kwds = "constr, wlsq" } @book{vanl:92, author = "C. F. {Van Loan}", year = "1992", title = "Computational Frameworks for the {Fourier} Transform", publisher = "SIAM", series = "Frontiers in Applied Mathematics", volume = "10", address = "Philadelphia", kwds = "fft, survey" } @article{vara:73, author = "J.M. Varah", year = "1973", title = "On the Numerical Solution of Ill-conditioned Linear Systems with Applications to Ill-posed Problems", journal = "SIAM J. Numer. Anal.", volume = "10", pages = "257--267", kwds = "illp, regul" } @article{vara:75, author = "J.M. Varah", year = "1975", title = "A Lower Bound for the Smallest Singular Value of a Matrix", journal = "Linear Algebra Appl.", volume = "11", pages = "1--2", kwds = "cond, svd" } @article{vara:79, author = "J.M. Varah", year = "1979", title = "A Practical Examination of some Numerical Methods for Linear Discrete Ill-posed Problems", journal = "SIAM Review", volume = "21", pages = "100--111", kwds = "illp, regul" } @article{vara:94, author = "J.M. Varah", year = "1994", title = "Backward Error Estimates for {Toeplitz} Systems", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "408--417", kwds = "err, toep" } @book{varg:62, author = "R. S. Varga", year = "1962", title = "Matrix Iterative Analysis", publisher = "Prentice-Hall", address = "Englewood Cliffs, NJ", kwds = "iter, survey" } @article{vava:94, author = "S. A. Vavasis", year = "1994", title = "Stable Numerical Algorithms for Equilibrium Systems", journal = "SIAM J. Matrix Anal. Appl.", volume = "15", pages = "1108--1131", kwds = "wlsq" } @phdthesis{matt:93, author = "U. von MATT", year = "1993", title = "Large Constrained Quadratic Problems", school = "Institute for Scientific Computing, ETH", address = "Z{\"u}rich, Switzerland", type = "{Ph. D.} thesis", kwds = "constr, nlsq" } @inproceedings{matt:95, author = "U. von Matt", year = "1995", title = "The Orthogonal {QD}-Algorithm", booktitle = "{SVD} and Signal Processing, III: Algorithms, Architectures and Applications", editor = "M. Moonen and B. {De Moor}", pages = "99--106", publisher = "Elsevier, Amsterdam", kwds = "svd" } @phdthesis{wald:94, author = "B. Wald\'en", year = "1994", title = "Least Squares Methods and Application in Robotics", school = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", type = "{Ph. D.} thesis", kwds = "regul, nlsq" } @article{waks:95, author = "B. Wald\'en and R. Karlsson and J.-G. Sun", year = "1995", title = "Optimal Backward Perturbation Bounds for the Linear Least Squares Problem", journal = "Numer. Linear Algebra Appl.", volume = "2", pages = "271--286", kwds = "err, pert" } @article{wamp:69, author = "R. H. Wampler", year = "1969", title = "An Evaluation of Linear Least Squares Computer Programs", journal = "J. Res. Nat. Bur. Standards", volume = "73B", pages = "59--90", kwds = "stat, regr, err, grsch, test" } @article{wamp:70, author = "R. H. Wampler", year = "1970", title = "A Report on the Accuracy of some Widely Used Least Squares Computer Programs", journal = "J. Amer. Statist. Assoc.", volume = "65", pages = "549--565", kwds = "err, test, grsch" } @inproceedings{wamp:72, author = "R. H. Wampler", year = "1972", title = "Some Recent Developments in Linear Least Squares Computations", booktitle = "Proceedings of the Computer Science and Statistics: Sixth Annual Symposium on the Interface", editor = "M.E. Tarter", publisher = "Academic Press, New York", pages = "94--110", kwds = "grsch, stat" } @article{wamp:79, author = "R. H. Wampler", year = "1979", title = "Solutions to Weighted Least Squares Problems by Modified {Gram--Schmidt} with Iterative Refinement", journal = "ACM Trans. Math. Software", volume = "5", pages = "457--465", kwds = "qrd, grsch, ir, wlsq" } @article{wamp:79a, author = "R. H. Wampler", year = "1979", title = "{L{\rm 2}A} and {L{\rm 2}B}, Weighted Least Squares Solutions by Modified {Gram--Schmidt} with Iterative Refinement", journal = "ACM Trans. Math. Software", volume = "5", pages = "494--99", kwds = "qrd, grsch, ir, wlsq, soft, weights" } @article{wamp:80, author = "R. H. Wampler", year = "1980", title = "Test Procedures and Test Problems for Least Squares Algorithms", journal = "J. Econom.", volume = "12", pages = "3--22", kwds = "test" } @phdthesis{wang:93, author = "X. Wang", year = "1993", title = "Incomplete Factorization Preconditioning for Least Squares Problems", school = "Department of Mathematics, University of Illinois at Urbana-Champaign", address = "Urbana, IL", type = "{Ph. D.} thesis", kwds = "iter, precond" } @article{wagb:96, author = "X. Wang and K. A. Gallivan and R. Bramley", year = "1996", title = "{CIMGS}: An Incomplete Orthogonal Factorization Preconditionier", journal = "SIAM J. Sci. Comput.", volume = "17", note = "to appear", pages = "", kwds = "iter, precond" } @inproceedings{wats:84, author = "G. A. Watson", year = "1984", title = "The Numerical Solution of Total $\ell_p$ Approximation Problems", booktitle = " Numerical Analysis. Proceedings of the 10th Biennial Conference Dundee, Scotland 1983", editor ="D.F. Griffiths", publisher = "Springer-Verlag, Berlin", series = " Lecture Notes in Mathematics", volume = "630", pages = "72--105", kwds = "rob" } @techreport{wedi:72a, author = "P.-{\AA}. Wedin", year = "1972", title = "The Non-Linear Least Squares Problem from a Numerical Point of View. {I} {Geometrical} Properties", institution = "Department of Computer Sciences, Lund University", address = "Lund, Sweden", type = "{Tech. Report}", number = "", kwds = "nlsq, pert" } @article{wedi:72, author = "P.-{\AA}. Wedin", year = "1972", title = "Perturbation Bounds in Connection with the Singular Value Decomposition", journal = "BIT", volume = "12", pages = "99--111", kwds = "svd, pert, rank" } @article{wedi:73a, author = "P.-{\AA}. Wedin", year = "1973", title = "On the Almost Rank Deficient Case of the Least Squares Problem", journal = "BIT", volume = "13", pages = "344--354", kwds = "pert, rank, svd" } @article{wedi:73b, author = "P.-{\AA}. Wedin", year = "1973", title = "Perturbation Theory for Pseudo-Inverses", journal = "BIT", volume = "13", pages = "217--232", kwds = "pert, rank, ginv" } @techreport{wedi:74, author = "P.-{\AA}. Wedin", year = "1974", title = "On the {Gauss-Newton} Method for the Nonlinear Least Squares Problems", institution = "Institute for Applied Mathematics", address = "Stockholm, Sweden", type = "Working Paper", number = "24", kwds = "nlsq" } @techreport{wedi:78, author = "P.-{\AA}. Wedin", year = "1978", title = "Perturbations of the Pseudo-Inverse and the Linear Least Squares Problem Analysed with Suitable Matrix Decompositions", institution = "Institute of Information Processing, University of Ume\aa", address = "Sweden", type = "{Tech. Report}", number = "UMINF--69.78", kwds = "pert, ginv" } @techreport{wedi:79, author = "P.-{\AA}. Wedin", year = "1979", title = "Notes on the Constrained Linear Least Squares Problem. {A} New Approach Based on Generalized Inverses", institution = "Institute of Information Processing, University of Ume\aa", address = "Sweden", type = "{Tech. Report}", number = "UMINF--75.79", kwds = "constr, ginv" } @techreport{wedi:85, author = "P.-{\AA}. Wedin", year = "1985", title = "Perturbation Theory and Condition Numbers for Generalized and Constrained Linear Least Squares Problems", institution = "Institute of Information Processing, University of Ume\aa", address = "Sweden", type = "{Tech. Report}", number = "UMINF--125.85", kwds = "pert, ginv, constr, cond, wlsq" } @article{wei:90, author = "M. Wei", year = "1990", title = "Perturbation of the Least Squares Problem", journal = "Linear Algebra Appl.", volume = "141", pages = "177--182", kwds = "pert" } @article{wei:92, author = "M. Wei", year = "1992", title = "The Analysis for the Total Least Squares Problems with More than One Solution", journal = "SIAM J. Matrix. Anal. Appl.", volume = "13", pages = "746--763", kwds = "tls, pert" } @article{wei:92a, author = "M. Wei", year = "1992", title = "Algebraic Relations Between the Total Least Squares and Least Squares Problems with More than One Solution", journal = "Numer. Math.", volume = "62", pages = "123--148", kwds = "tls, pert" } @article{wei:92b, author = "M. Wei", year = "1992", title = "Algebraic Properties of the Rank-Deficient Equality Constrained and Weighted Least Squares Problem", journal = "Linear Algebra Appl.", volume = "161", pages = "27--43", kwds = "constr, pert" } @article{wei:92c, author = "M. Wei", year = "1992", title = "Perturbation Theory for the Rank-Deficient Equality Constrained and Weighted Least Squares Problem", journal = "SIAM J. Numer. Anal.", volume = "29", pages = "1462--1481", kwds = "constr, pert" } @article{weke:71, author = "P. R. Weil and P. C. Kettler", year = "1971", title = "Rearranging Matrices to Block-angular Form for Decomposition (and other) Algorithms", journal = "Management Sci.", volume = "18", pages = "98--108", kwds = "sparse, perm" } %wi- @book{wilk:63, author = "J. H. Wilkinson", year = "1963", title = "Rounding Errors in Algebraic Processes", publisher = "Prentice-Hall", address = "Englewood Cliffs, NJ", kwds = "err, lud, survey" } @book{wilk:65, author = "J. H. Wilkinson", year = "1965", title = "The Algebraic Eigenvalue Problem", publisher = "Clarendon Press", address = "Oxford, UK", kwds = "nla, eig, err, survey" } @incollection{wilk:65a, author = "J. H. Wilkinson", year = "1965", title = "Error Analysis of Transformations Based on the Use of Matrices of the Form {$I-2xx^{\rm H}$}", booktitle = "Error in Digital Computation", editor = "L. B. Rall", publisher = "John Wiley, New York", pages = "77--101", kwds = "err, house" } @inproceedings{wilk:68, author = "J. H. Wilkinson", year = "1968", title = "A Priori Error Analysis of Algebraic Processes", booktitle = "Proceedings International Congress Math.", publisher = "Izdat. Mir, Moscow", pages = "629--639.", kwds = "chol, err" } @article{wilk:71, author = "J. H. Wilkinson", year = "1971", title = "Modern Error Analysis", journal = "SIAM Review", volume = "13", pages = "548--568", kwds = "error, hist, survey" } @techreport{wilk:77a, author = "J. H. Wilkinson", year = "1977", title = "The Use of Single Precision-Residuals in the Solution of Linear Systems", institution = "National Physical Laboratory", address = "Teddington, UK", type = "unpublished report", kwds = "ir, err" } @inproceedings{wilk:77, author = "J. H. Wilkinson", year = "1977", title = "Some recent advances in numerical linear algebra", pages = "1--53", booktitle = "The State of the Art in Numerical Analysis", editor = "D.A.H. Jacobs", publisher = "Academic Press, New York", kwds = "nla" } @article{wilk:86, author = "J. H. Wilkinson", year = "1986", title = "Error Analysis Revisited", journal = "IMA Bulletin", volume = "22", pages = "192--200", kwds = "error, hist" } @book{wire:71, author = "J. H. Wilkinson and C. Reinsch", year = "1971", title = "Handbook for Automatic Computation Volume II. Linear Algebra", publisher = "Springer-Verlag", address = "New York", kwds = "nla, soft, eig, svd, qrd, survey" } @article{witt:36, author = "H. Wittmeyer", year = "1936", title = "{E}influss der {{\"A}nderung} einer {M}atrix auf der {L}{\"o}sung des zugeh{\"o}rigen {G}leichungssystems, sowie auf die charakterischen {Z}ahlen und die {E}igenvektoren", journal = "Z. Angew. Math. Mech.", volume = "16", pages = "189--199", kwds = "err" } @article{wrho:85, author = "S. J. Wright and J. N. Holt", year = "1985", title = "Algorithms for Nonlinear Least Squares with Linear Inequality Constraints", journal = "SIAM J. Sci. Statist. Comput.", volume = "6", pages = "1033--1048", kwds = "nlsq, constr" } @article{yopa:96, author = "K. Yoo and H. Park", year = "1996", title = "Accurate Downdating of a modified {Gram-Schmidt QR} Decomposition", journal = "BIT", volume = "36", pages = "166--181", kwds = "downd, qrd, grsch" } @book{youn:71, author = "D. M. Young", year = "1971", title = "Iterative Solution of Large Linear Systems", publisher = "Academic Press", address = "New York", kwds = "iter, survey" } @phdthesis{yuan:93, author = "J.-Y. Yuan", year = "1993", title = "Iterative Methods for the Generalized Least-Squares Problem", school = "Instituto de Matem\'atica Pura e Aplicada", address = " Rio de Janeiro, Brazil", type = "{Ph. D.} thesis", kwds = "iter, thesis" } @article{yuan:93a, author = "J.-Y. Yuan", year = "1993", title = "The Convergence of the {\rm 2}-block {SAOR} Method for the Least-Squares Problem ", journal = "Appl. Numer. Math.", volume = "11", pages = "429--441", kwds = "iter" } %za- @article{zha:91, author = "H. Zha", year = "1991", title = "Implicit {QR} Factorization of a Product of Three Matrices", journal = "BIT", volume = "31", pages = "375--379", kwds = "qrd, ginv, test" } @article{zha:91a, author = "H. Zha", year = "1991", title = "Restricted Singular Value Decomposition of Matrix Triples", journal = "SIAM J. Matrix Anal. Appl.", volume = "12", pages = "172--194", kwds = "qrd, ginv, test" } @article{zha:92, author = "H. Zha", year = "1992", title = "A Two-way Chasing Scheme for Reducing a Symmetric Arrowhead Matrix to Tridiagonal Form", journal = "J. Numerical Linear Algebra Appl.", volume = "1", pages = "49--57", kwds = "svd, upd" } @article{zha:93, author = "H. Zha", year = "1993", title = "A Componentwise Perturbation Analysis of the {$QR$} Decomposition", journal = "SIAM J. Matrix Anal. Appl.", volume = "14", pages = "1124--1131", kwds = "qrd, pert" } @incollection{zele:62, author = "M. Zelen", year = "1962", title = "Linear Estimation and Related Topics", booktitle = "Survey of Numerical Analysis", editor = "J. Todd", publisher = "McGraw-Hill, New York", pages = "558--584", kwds = "stat, hist" } @article{ziel:86, author = "G. Zielke", year = "1986", title = "Report on Test Matrices for Generalized Inverses", journal = "Computing", volume = "36", pages = "105--162", kwds = "ginv, test" } @phdthesis{zimm:77, author = "P. Zimmermann", year = "1977", title = "{Ein Algorithmus zur L{\"o}sung linearer Least Squares Probleme mit unteren und oberen Schranken als Nebenbedingungen}", school = "Universit{\"a}t W{\"u}rzburg", address = "Germany", institution = "Institut f{\"u}r Angewandte Mathematik und Statistik", type = "{D}iplomarbeit", kwds = "constr" } @article{zlat:82, author = "Z. Zlatev", year = "1982", title = "Comparison of Two Pivotal Strategies in Sparse Plane Rotations", journal = " Comput. Math. Appl.", volume = "8", pages = "119--135", kwds = "sparse, perm, rot" } @book{zlat:92, author = "Z. Zlatev", year = "1992", title = "Computational Methods for General Sparse Matrices", publisher = "Kluwer Academic Publishers", address = "Norwell, MA", kwds = "sparse, perm, rot" } @techreport{zlni:79, author = "Z. Zlatev and H. Nielsen", year = "1979", title = "{LLSS{\rm 01}} - A {Fortran} Subroutine for Solving Least Squares Problems ({User's} Guide)", institution = "Institute of Numerical Analysis, Technical University of Denmark", address = "Lyngby, Denmark", type = "{Tech. Report}", number = "79-07", kwds = "soft, sparse" } @article{zlni:88, author = "Z. Zlatev and H. Nielsen", year = "1988", title = "Solving Large and Sparse Linear Least-Squares Problems by Conjugate Gradient Algorithms", journal = "Comput. Math. Appl.", volume = "15", pages = "185--202", note = "", kwds = "cg, precond, sparse, iter" } @unpublished{altkeys, author = "Zzzzz, Rip van", year = "1991", title = "Alternate Key Words", kwds = "augmented system (augms) backward perturbation (pert), banded least squares (band), blas (blas), block angular system (basys), block methods (block), Chebyshev approximation (cheb), Cholesky (chol), condition (cond), conjugate gradients (cg), constrained least squares (constr), control theory (contr), covariance matrix (covar), CS decomposition (csd), downdating (downd), equilibration (scale), error estimate (err), generalized eigenvalue problems (geig), fill-in (fill), generalized inverse (ginv), generalized linear model (glsq), generalized QR decomposition (gqrd), geodesy (geod), generalized singular value decomposition (gsvd), Givens rotation (rot), graph theory (graph), Gram-Schmidt (grsch), history of least squares ( hist), Householder (house), hyperbolic rotation (hyp), ill-posed (regul), interior point methods (intpoint), interval analysis (err), iterative method (iter), iterative refinement (ir), Lanczos (lanczos), linear algebra general (la), LU decomposition (lud), matrix approximation (max), nested dissection (nestdis), nonlinear least squares (nlsq), normal equations (ne), numerical linear algebra (nla) optimization (opt), ordering for sparsity (perm), orthogonalization (orth), orthogonal regression (orthreg), precision (err), preconditioning (precond), pseudo-inverse (ginv), parallel computation (prll), perturbation theory (pert), polynomial approximation (poly) projection (orth), QR decomposition (qrd), quadratic programming (quadpr), random matrix (rand), rank degenerate problems (rank), rank revealing QR factorization (rrqrd), recursive least squares (rls), regularization (regul), regression (regr), robust estimation (rob), scaling (scale), signal processing (sigp), singular value decomposition (svd), spline approximation (spline), survey paper/book (survey), systolic (syst), software (soft), sparse (sparse), statistics (stat), test matrix (test), Toeplitz (toep), total least squares (tls), underdetermined systems (uds), updating (upd), variable projection (varpro), vector processing (prll), weighted least squares (wlsq)" }