LEAST-SQUARES APPROXIMATION BY ELEMENTS FROM MATRIX ORBITS ACHIEVED BY GRADIENT FLOWS ON COMPACT LIE GROUPS
Chi-Kwong Li, Yiu‐Tung Poon, Thomas Schulte-herbrüggen · 2008
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 A0 by the sum of matrices in S(A1),..., S(AN) in the sense of finding the Euclidean least-squares distance min n ‚‚X1 o + · · · + XN − A0 ‚ : Xj ∈ S(Aj), j = 1,..., N. Connections of the results to different pure and applied areas are discussed. 1.