On a variational formulation of the generalized singular value decomposition

被引：23

作者：

Chu, MT

Funderlic, RE

Golub, GH

机构：

[1] N CAROLINA STATE UNIV, DEPT COMP SCI, RALEIGH, NC 27695 USA

[2] STANFORD UNIV, DEPT COMP SCI, STANFORD, CA 94305 USA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1997年 / 18卷 / 04期

关键词：

generalized eigenvalue and eigenvector; generalized singular value and singular vector; stationary value and stationary point; deflation; duality;

D O I：

10.1137/S0895479895287079

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A variational formulation for the generalized singular value decomposition (GSVD) of a pair of matrices A is an element of R-mxn and B is an element of R-pxn is presented. In particular, a duality theory analogous to that of the SVD provides new understanding of left and right generalized singular vectors. It is shown that the intersection of row spaces of A and B plays a key role in the GSVD duality theory. The main result that characterizes left GSVD vectors involves a generalized singular value deflation process.

引用

页码：1082 / 1092

页数：11

共 10 条

[1]

ANSTROM B, 1984, BIT, V24, P568

[2] COMPUTING THE GENERALIZED SINGULAR-VALUE DECOMPOSITION [J].