Matrix form of the CGS method for solving general coupled matrix equations

被引：53

作者：

Hajarian, Masoud ^{[1
]}

机构：

[1] Shahid Beheshti Univ, Fac Math Sci, Dept Math, Tehran 19839, Iran

来源：

APPLIED MATHEMATICS LETTERS | 2014年 / 34卷

关键词：

Iterative method; CGS method; Linear system; Kronecker product; Vectorization operator; LEAST-SQUARES SOLUTIONS; ITERATIVE ALGORITHM; LINEAR-SYSTEMS; AXB; NORM; CYD;

D O I：

10.1016/j.aml.2014.03.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the problem of solving the general coupled matrix equations [GRAPHICS] A(ij)X(j)B(ij) = C-i, i = 1, 2,..., p, (including several linear matrix equations as special cases) which plays important roles in system and control theory. Based on the conjugate gradients squared (CGS) method, a simple and efficient matrix algorithm is derived to solve the general coupled matrix equations. The derived iterative algorithm is illustrated by two numerical examples and is compared with other popular iterative solvers in use today. (C) 2014 Elsevier Ltd. All rights reserved.

引用

收藏

页码：37 / 42

页数：6

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