An efficient method for special least squares solution of the complex matrix equation (AXB, CXD) = (E, F)

被引：7

作者：

Zhang, Fengxia ^{[1
]}

Wei, Musheng ^{[1
,2
]}

Li, Ying ^{[1
]}

Zhao, Jianli ^{[1
]}

机构：

[1] Liaocheng Univ, Coll Math Sci, Liaocheng 252000, Shandong, Peoples R China

[2] Shanghai Normal Univ, Coll Math & Sci, Shanghai 200234, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 76卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Complex matrix equation; Least squares Hermitian solution; Real representation matrix; Moore-Penrose generalized inverse; HERMITIAN SOLUTION; SYMMETRIC-SOLUTIONS; GENERAL-SOLUTION; SOLUTION SETS; NORM; ALGORITHM; PAIR; A1XB1=C1; SYSTEMS;

D O I：

10.1016/j.camwa.2018.07.044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose an efficient method for special least squares solution of the complex matrix equation (AXB, CXD) = (E, F). By using the real representation matrices of complex matrices, the particular structure of the real representation matrices, the Moore Penrose generalized inverse and the Kronecker product, we obtain the explicit expression of the minimal norm least squares Hermitian solution of the complex matrix equation (AXB, CXD) = (E, F), which was studied by a product of matrices and vectors in Wang et al. (2016). Our resulting formulas only involve real matrices, and the corresponding algorithm only performs real arithmetic. Therefore our proposed method is more effective and portable. Finally, we give three numerical examples to illustrate the effectiveness of our proposed method. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：2001 / 2010

页数：10

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