A system of matrix equations with five variables

被引：12
作者：
Rehman, Abdur [1 ,2 ]
Wang, Qing-Wen [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Univ Engn & Technol, Lahore, Pakistan
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 271卷
基金：
中国国家自然科学基金;
关键词：
Matrix equation; General solution; Qudiernion matrix; Moore-Penrose inverse; Rank; ITERATIVE METHOD; GENERAL-SOLUTION; REGULARIZATION; SOLVABILITY;
D O I：
10.1016/j.amc.2015.09.066
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give some necessary and sufficient conditions for the consistence of the system of quaternion matrix equations A(1)X = C-1, YB1 = D-1, A(2)W = C-2, ZB(2) = D-2, A(3)V = C-3, VB3 = C-4, A(4)VB(4) = C-5, A(5)X + YB5 + C6W + ZD(6) + E6VF6 = G(6), and constitute an expression of the general solution to the system when it is solvable. The outcomes of this paper encompass some recognized results in the collected works. In addition, we establish an algorithm and a numerical example to illustrate the theory constructed in the paper. In this paper, we give some necessary and sufficient conditions for the consistence of the system of quaternion matrix equations (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：805 / 819
页数：15
相关论文
共 55 条
[41]   The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes [J].
Took, Clive Cheong ;
Mandic, Danilo P. .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2009, 57 (04) :1316-1327
[42]   ON THE MATRIX EQUATION AX = B WITH APPLICATIONS TO THE GENERATORS OF A CONTROLLABILITY MATRIX [J].
UHLIG, F .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 85 :203-209
[43]   ALMOST NONINTERACTING CONTROL BY MEASUREMENT FEEDBACK [J].
VANDERWOUDE, JW .
SYSTEMS & CONTROL LETTERS, 1987, 9 (01) :7-16
[44]   P-(skew) symmetric common solutions to a pair of quaternion matrix equations [J].
Wang, Qing-Wen ;
Chang, Hai-Xia ;
Lin, Chun-Yan .
APPLIED MATHEMATICS AND COMPUTATION, 2008, 195 (02) :721-732
[45]   Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications [J].
Wang, Qing-Wen ;
Yu, Shao-Wen ;
Lin, Chun-Yan .
APPLIED MATHEMATICS AND COMPUTATION, 2008, 195 (02) :733-744
[46]   Systems of coupled generalized Sylvester matrix equations [J].
Wang, Qing-Wen ;
He, Zhuo-Heng .
AUTOMATICA, 2014, 50 (11) :2840-2844
[47]   Solvability conditions and general solution for mixed Sylvester equations [J].
Wang, Qing-Wen ;
He, Zhuo-Heng .
AUTOMATICA, 2013, 49 (09) :2713-2719
[48]   Some matrix equations with applications [J].
Wang, Qing-Wen ;
He, Zhuo-Heng .
LINEAR & MULTILINEAR ALGEBRA, 2012, 60 (11-12) :1327-1353
[49]   A system of matrix equations and its applications [J].
Wang QingWen ;
He ZhuoHeng .
SCIENCE CHINA-MATHEMATICS, 2013, 56 (09) :1795-1820
[50]   Solution to generalized sylvester matrix equations [J].
Wu, Ai-Guo ;
Duan, Guang-Ren ;
Zhou, Bin .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (03) :811-815
123456