A TREE OF GENERALIZATIONS OF THE ORDINARY SINGULAR VALUE DECOMPOSITION

被引：45

作者：

DEMOOR, B

ZHA, HY

机构：

[1] STANFORD UNIV,DEPT ELECT ENGN,STANFORD,CA 94305

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

[3] LONRAD ZUSE ZENTRUM INFORMAT TECH BERLIN,BERLIN,GERMANY

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1991年 / 147卷

关键词：

D O I：

10.1016/0024-3795(91)90243-P

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown how to generalize the ordinary singular value decomposition of a matrix into a combined factorization of any number of matrices. We propose to call these factorizations generalized singular value decompositions. For two matrices, this reduces to the product and quotient singular value decompositions. One of the factorizations for three matrices is the restricted singular value decomposition. These generalizations form a tree of factorizations, where at level k, for k matrices, there are 2k factorizations, not all of which are independent. The different levels are related to each other in a recursive fashion. Any generalized singular value decomposition for k matrices can be constructed from a decomposition for k - 1 matrices. This results in an inductive proof which uses only the ordinary singular value decomposition. Several examples are analysed in detail.

引用

页码：469 / 500

页数：32

共 15 条

[1]

AUTONNE L, 1902, B SOC MATH FRANCE, V30, P121

[2]

BELTRAMI E., 1873, GIORNALE MATH, V11, P98

[3]

DEMOOR B, 1989, ESATSISTA198910 KATH

[4]

DEMOOR B, 1989, ESATSISTA198912 KATH

[5]

DEMOOR B, IN PRESS SIAM J MATR

[6]

Deprettere EFA, 1988, SVD SIGNAL PROCESSIN

[7]

FERNANDO KV, NAG TR887 TECHN REP

[8]

Golub G.H., 1983, MATRIX COMPUTATIONS

[9] COMPUTING THE SINGULAR VALUE DECOMPOSITION OF A PRODUCT OF 2 MATRICES [J].

HEATH, MT ;

LAUB, AJ ;

PAIGE, CC ;

WARD, RC .

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1986, 7 (04) :1147-1159

[10]

Jordan C., 1874, J MATH PURE APPL, V19, P35

← 1 2 →