Matrix Approximation

Henry Wolkowicz's Research

Research Home	Publications & Abstracts	Talks & Presentations	Semidefinite Programming	EDM and SNL	Graph Partitioning	Maximum Cut
Linear Programming	Quadratic Assignment	NLP, Regularization, TRS	Set Partitioning	Matrix Approximation	Misc. Software/Opt.	Matrices and Optimization

Matrix Approximation Problems Using SDP

Positive Semidefinite Matrix Completion Problems

Suppose that we are given a partial Hermitian matrix,
i.e., some of the elements are fixed while others are free.

The matrix completion problem consists in finding the free elements
in order to satisfy a criterion such as positive semidefiniteness.

A characterization of existence of completions using chordality is given in this paper.

The approximate positive semidefinite completion problem.

A gzipped tar file with MATLAB programs that solve the AC problem is also available in this directory.
In particular, the file dualcomp.m is a self-documented MATLAB file that solves the large sparse approximate completion problem in the case that there are many elements free.

Linked from Decision Tree for Optimization Software - NLP/SDP/Appl.

Researchers in Matrix Theory and Related Areas

Alan Edelman, MIT
Grassman manifolds, Kronecker form, matrix pencils

Volker Mehrmann, Technische Universitat, Berlin
Completion problems, control theory, matrix pencils

G.W. (Pete) Stewart, University of Maryland
Numerical analysis

Clark Wells
Molecular conformation problems

A bib file with references on
AC and EDM and SDP in general.

Euclidean Distance Matrix Completion Problems

T he approximate distance matrix completion problem

Characterizations of EDM.

A gzipped tar file containing MATLAB programs that solve the EDM problem is available in this directory.