The *congruence class of the solutions of some matrix equations

被引：24

作者：

Zheng, Bing ^{[1
]}

Yea, Lijuan ^{[1
]}

Cvetkovic-Ilic, Dragana S. ^{[2
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[2] Univ Nis, Fac Sci, Dept Math, Nish, Serbia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2009年 / 57卷 / 04期

关键词：

Matrix equation; *Congruence class; Singular Value Decomposition (SVD); Generalized Singular Value Decomposition (GSVD); Frobenius norm; NONNEGATIVE-DEFINITE; AXA-ASTERISK;

D O I：

10.1016/j.camwa.2008.11.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The *congruence class of a least square solution for the following matrix equations AX = B, A*XA = D, AXB = D and (AX XB) = (E F) is presented. Also, we derive necessary and sufficient conditions for the existence of a least square solution and present a general form of such solutions using the Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). Crown Copyright (C) 2008 Published by Elsevier Ltd. All rights reserved.

引用

页码：540 / 549

页数：10

共 22 条

[1]

[Anonymous], 1996, Iterative Methods for Sparse Linear Systems

[2] SYMMETRIC-SOLUTIONS OF LINEAR MATRIX EQUATIONS BY MATRIX DECOMPOSITIONS [J].

CHU, KWE .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1989, 119 :35-50

[3] Positive and real-positive solutions to the equation axa* = c in C*-algebras [J].

Cvetkovic-Ilic, D. ;

Dajic, Alegra ;

Koliha, J. J. .

LINEAR & MULTILINEAR ALGEBRA, 2007, 55 (06) :535-543

[4] Re-nnd solutions of the matrix equation A X B=C [J].

Cvetkovic-Ilic, Dragana S. .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2008, 84 (01) :63-72

[5]

DAI H, 1996, LINEAR ALGEBRA APPL, V246, P31

[6]

DAJIC A, EQUATIONS AX C XB D

[7] A TREE OF GENERALIZATIONS OF THE ORDINARY SINGULAR VALUE DECOMPOSITION [J].

DEMOOR, B ;

ZHA, HY .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 147 :469-500

[8] Least squares solution of BXAT = T over symmetric, skew-symmetric, and positive semidefinite X [J].

Deng, YB ;

Hu, XY ;

Zhang, L .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 25 (02) :486-494

[9]

Friswell MI, 1995, Finite element model updating in structural dynamics

[10]

[郭翠平 Guo Cuiping], 2004, [高等学校计算数学学报, Numerical Mathematics A Journal of Chinese University], V26, P222

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