Least-squares solutions to the matrix equations AX = B and XC = D

被引：25

作者：

Yuan, Yongxin ^{[1
]}

机构：

[1] Jiangsu Univ Sci & Technol, Sch Math & Phys, Zhenjiang 212003, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 216卷 / 10期

关键词：

Matrix equation; Least-squares solution; Symmetric solution; SINGULAR VALUE; DECOMPOSITION; REFLEXIVE; SYSTEMS; XB;

D O I：

10.1016/j.amc.2010.04.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The least-squares solution and the least-squares symmetric solution with the minimum-norm of the matrix equations AX = B and XC = D are considered in this paper. By the matrix differentiation and the spectral decomposition of matrices, an explicit representation of such solution is given. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3120 / 3125

页数：6

共 50 条

[21] An expression of the general common least-squares solution to a pair of matrix equations with applications
Liu, Xifu
Yang, Hu
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (10) : 3071 - 3078
[22] Relations between least-squares and least-rank solutions of the matrix equation AXB = C
Tian, Yongge
Wang, Hongxing
APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (20) : 10293 - 10301
[23] Iterative algorithms for least-squares solutions of a quaternion matrix equation
Ahmadi-Asl, Salman
Beik, Fatemeh Panjeh Ali
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2017, 53 (1-2) : 95 - 127
[24] Norm-constrained least-squares solutions to the matrix equation AXB=C
Xu, Anbao
Peng, Zhenyun
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE OF MATRICES AND OPERATORS (MAO 2012), 2012, : 136 - 139
[25] Weighted least squares solutions to general coupled Sylvester matrix equations
Zhou, Bin
Li, Zhao-Yan
Duan, Guang-Ren
Wang, Yong
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 224 (02) : 759 - 776
[26] The best approximation problems between the least-squares solution manifolds of two matrix equations
Chen, Yinlan
Lan, Yawen
AIMS MATHEMATICS, 2024, 9 (08): : 20939 - 20955
[27] Least-squares partially bisymmetric solutions of coupled Sylvester matrix equations accompanied by a prescribed submatrix constraint
Hajarian, Masoud
Chronopoulos, Anthony Theodore
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (06) : 4297 - 4315
[28] 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
[29] Matrix rank/inertia formulas for least-squares solutions with statistical applications
Tian, Yongge
Jiang, Bo
SPECIAL MATRICES, 2016, 4 (01): : 130 - 140
[30] Analogs of Cramer's rule for the minimum norm least squares solutions of some matrix equations
Kyrchei, Ivan
APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (11) : 6375 - 6384

← 1 2 3 4 5 →