Conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations

被引：35
作者：
Zhang, Huamin [1 ]
Yin, Hongcai [2 ]
机构：
[1] Bengbu Univ, Dept Math & Phys, Bengbu 233030, Peoples R China
[2] Anhui Univ Finance & Econ, Sch Management Sci & Engn, Bengbu 233000, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 73卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Generalized coupled Sylvester matrix equations; Conjugate gradient least squares algorithm; Inner product space; FINITE ITERATIVE ALGORITHMS; REFLEXIVE SOLUTIONS; OPTIMAL APPROXIMATION; SYSTEMS; CONVERGENCE; AXB; CYD;
D O I：
10.1016/j.camwa.2017.03.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper discusses the conjugate gradient least squares algorithm for solving the generalized coupled Sylvester matrix equations Sigma(q)(j=1) A(ij)X(j)B(ij) = F-i, i = 1, 2, . . . ,p. We prove that if this system is consistent then the iterative solution converges to the exact solution and if this system is inconsistent then the iterative solution converges to the least squares solution within the finite iteration steps in the absence of the roundoff errors. Also by setting the initial iterative value properly we prove that the iterative solution converges to the least squares and minimum-norm solution. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2529 / 2547
页数：19
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