Least-squares Hermitian problem of complex matrix equation (AXB, CXD) = (E, F)

被引：0

作者：

Wang, Peng ^{[1
,2
]}

Yuan, Shifang ^{[1
]}

Xie, Xiangyun ^{[1
]}

机构：

[1] Wuyi Univ, Sch Math & Computat Sci, Jiangmen 529020, Peoples R China

[2] Wuhan Univ Technol, Sch Comp Sci & Technol, Wuhan 430070, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2016年

关键词：

matrix equation; least-squares solution; Hermitian matrices; Moore-Penrose generalized inverse; MINIMUM-NORM;

D O I：

10.1186/s13660-016-1231-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a direct method to solve the least-squares Hermitian problem of the complex matrix equation (AXB, CXD) = (E, F) with complex arbitrary coefficient matrices A, B, C, D and the right-hand side E, F. This method determines the least-squares Hermitian solution with the minimum norm. It relies on a matrix-vector product and the Moore-Penrose generalized inverse. Numerical experiments are presented which demonstrate the efficiency of the proposed method.

引用

页数：13

共 50 条

[41] LEAST-SQUARES SOLUTION OF AXB = DOVER SYMMETRIC POSITIVE SEMIDEFINITE MATRICES X
Anping Liao (Department of Mathematics and Information Science
Journal of Computational Mathematics, 2003, (02) : 175 - 182
[42] Least squares solutions of matrix equation AXB = C under semi-tensor product
Wang, Jin
ELECTRONIC RESEARCH ARCHIVE, 2024, 32 (05): : 2976 - 2993
[43] Common least-squares solution to some matrix equations
REHMAN Abdur
WANG Qingwen
上海大学学报(自然科学版), 2017, 23 (02) : 267 - 275
[44] Least-squares κ-skew-Hermitian solutions of matrix equations (AX = B,XC = D)
Li, Fan-Liang
Hu, Xi-Yan
Zhang, Lei
PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON MATRIX ANALYSIS AND APPLICATIONS, VOL 2, 2009, : 9 - 12
[45] An efficient method for least-squares problem of the quaternion matrix equation X - A(X)over-capB = C
Zhang, Fengxia
Wei, Musheng
Li, Ying
Zhao, Jianli
LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (13) : 2569 - 2581
[46] The least-squares solutions of inconsistent matrix equation over symmetric and antipersymmetric matrices
Xie, DX
Sheng, YP
Hu, XY
APPLIED MATHEMATICS LETTERS, 2003, 16 (04) : 589 - 598
[47] On solutions of matrix equation AXB+CYD = F
Xu, GP
Wei, MS
Zheng, DS
LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 279 (1-3) : 93 - 109
[48] Least-squares solutions to the matrix equations AX = B and XC = D
Yuan, Yongxin
APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (10) : 3120 - 3125
[49] The least-squares solutions of matrix equation (AXAT, BXBT) = (C, D) over bisymmetric matrices
Sheng, Yan-Ping
Tian, Ru
PROCEEDINGS OF 2009 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-6, 2009, : 473 - 475
[50] Conjugate Gradient Algorithm for Least-Squares Solutions of a Generalized Sylvester-Transpose Matrix Equation
Tansri, Kanjanaporn
Chansangiam, Pattrawut
SYMMETRY-BASEL, 2022, 14 (09):

← 1 2 3 4 5 →