THE PROCRUSTES PROBLEM FOR ORTHOGONAL STIEFEL MATRICES

被引：18

作者：

Bojanczyk, A. W. ^{[1
]}

Lutoborski, A. ^{[2
]}

机构：

[1] Cornell Univ, Dept Elect Engn, Ithaca, NY 14853 USA

[2] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 1999年 / 21卷 / 04期

关键词：

Procrustes problem; Stiefel manifolds; projections on ellipsoids; relaxation methods;

D O I：

10.1137/S106482759630992X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the Procrustes problem on the manifold of orthogonal Stiefel matrices. Given matrices A is an element of R-mxk; B is an element of R-mxp, m >= p >= k; we seek the minimum of parallel to A - BQ parallel to(2) for all matrices Q is an element of R-pxk; Q(T)Q = I-kxk. We introduce a class of relaxation methods for generating sequences of approximations to a minimizer and offer a geometric interpretation of these methods. Results of numerical experiments illustrating the convergence of the methods are given.

引用

页码：1291 / 1304

页数：14

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