Title

Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

Document Type

Article

Department/Program

Mathematics

Journal Title

Mathematics of Computation

Pub Date

2011

Volume

80

Issue

275

First Page

1601

Abstract

Let S(A) denote the orbit of a complex or real matrix A under a certain equivalence relation such as unitary similarity, unitary equivalence, unitary congruences etc. Efficient gradient-flow algorithms are constructed to determine the best approximation of a given matrix A(0) by the sum of matrices in S(A(1)), ... , S(A(N)) in the sense of finding the Euclidean least-squares distance min {parallel to X(1) + ... + X(N) - A(0)parallel to : X(j) is an element of S(A(j)), j = 1, ... , N}. Connections of the results to different pure and applied areas are discussed.

DOI

10.1090/S0025-5718-2010-02450-0

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