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Yu. Nesterov
Recent progress in efficient approximation of joint spectral radius.
The joint spectral radius of a set of matrices is a measure of
the maximal asymptotic growth rate that can be obtained by
forming long products of matrices taken from the set. This
quantity appears in a number of application contexts but is
notoriously difficult to compute and to approximate. We introduce
in this paper a procedure for approximating the joint spectral
radius of a finite set of matrices with arbitrary high relative
accuracy. Our approximation procedure is polynomial in the size
of the matrices once the number of matrices and the desired
accuracy are fixed. An essential element of our technique is a
semidefinite lifting of linear operators.