Weighted least squares solutions to general coupled Sylvester matrix equations

被引：115

作者：

Zhou, Bin ^{[1
]}

Li, Zhao-Yan ^{[2
]}

Duan, Guang-Ren ^{[1
]}

Wang, Yong ^{[2
]}

机构：

[1] Harbin Inst Technol, Ctr Control Theory & Guidance Technol, Harbin 150001, Peoples R China

[2] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 224卷 / 02期

关键词：

Weighted least squares solutions; Weighted generalized inverses; Coupled Sylvester matrix equations; Gradient based iterative algorithms; Maximal convergence rate; ITERATIVE SOLUTIONS; LYAPUNOV EQUATIONS; SYMMETRIC SOLUTION; LINEAR-SYSTEMS; AXB; REFLEXIVE; ALGORITHM;

D O I：

10.1016/j.cam.2008.06.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with weighted least squares Solutions to general coupled Sylvester matrix equations. Gradient based iterative algorithms are proposed to solve this problem. This type of iterative algorithm includes a wide class of iterative algorithms, and two special cases of them are studied in derail in this paper. Necessary and sufficient conditions guaranteeing the convergence of the proposed algorithms are presented. Sufficient conditions that are easy to compute are also given. The optimal step sizes such that the convergence rates of the algorithms, which are properly defined in this paper, are maximized and established. Several special cases of the weighted least Squares problem, Such as a least squares Solution to the coupled Sylvester matrix equations problem, solutions to the general coupled Sylvester matrix equations problem, and a Weighted least squares Solution to the linear matrix equation problem are simultaneously solved. Several numerical examples are given to illustrate the effectiveness of the proposed algorithms. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：759 / 776

页数：18

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