An Iteration Method for Solving the Inconsistent Matrix Equation [ATXA, BTXB]=[C, D] over Symmetric Matrices

被引：0

作者：

Lei, Yuan ^{[1
]}

Liao, An-Ping ^{[1
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

来源：

ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL II: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS | 2008年

关键词：

Matrix equation; Iteration method; Least-squares solution; Minimum norm solution;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an iteration method with short recurrences is presented to solve the inconsistent matrix equation [A(T) XA, B-T XB] = [C, D]. The minimization property of this iteration method is characterized by constructing a kind of special matrix function, and the fact that the norm of the residual sequence is strictly monotone decreasing is proved.

引用

页码：140 / 143

页数：4

共 7 条

[1] THE SYMMETRICAL SOLUTION OF THE MATRIX EQUATIONS AX + YA = C, AXAT + BYBT = C, AND (ATXA, BTXB) = (C, D) [J].

CHANG, XW ;

WANG, JS .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 179 :171-189

[2] Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations [J].

Deng, Yuan-Bel ;

Bai, Zhong-Zhi ;

Gao, Yong-Hua .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2006, 13 (10) :801-823

[3] The matrix nearness problem for symmetric matrices associated with the matrix equation [ATXA, BTXB] = [C, D] [J].

Liao, An-ping ;

Lei, Yuan ;

Yuan, Shi-fang .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 418 (2-3) :939-954

[4] An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C [J].

Peng, YX ;

Hu, XY ;

Zhang, L .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 160 (03) :763-777

[5] An efficient iterative method for solving the matrix equation AXB plus CYD = E [J].

Peng, Zhen-yun ;

Peng, Ya-xin .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2006, 13 (06) :473-485

[6]

WANG RS, 2003, FUNCTIONAL ANAL OPTI

[7]

[袁永新 Yuan Yongxin], 2002, [高等学校计算数学学报, Numerical Mathematics A Journal of Chinese University], V24, P127

← 1 →