#### 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.

#### Recommended Citation

Li, Chi-Kwong; Poon, Yiu-Tung; and Schulte-Herbrueggen, Thomas, Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups (2011). *Mathematics of Computation*, 80(275), 1601-1621.

10.1090/S0025-5718-2010-02450-0

#### DOI

10.1090/S0025-5718-2010-02450-0