The extremal solution of the matrix equation Xs + A*X-qA = I

被引：6

作者：

Wang, Minghui ^{[1
]}

Wei, Musheng ^{[2
]}

Hu, Shanrui ^{[1
]}

机构：

[1] Qingdao Univ Sci & Technol, Dept Math, Qingdao 266061, Peoples R China

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 220卷

基金：

中国国家自然科学基金;

关键词：

Positive definite matrix; Nonlinear matrix equation; Iterative algorithm; The maximal solution; The minimal solution; POSITIVE-DEFINITE SOLUTION; EXISTENCE;

D O I：

10.1016/j.amc.2013.06.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the distribution of the positive definite solution of the nonlinear equation X-s + A*X(-q)A = I is deduced, the existence of the maximal solution and the minimal solution is discussed and two new iterative algorithms for obtaining these solutions are proposed. These algorithms avoid matrix inversion. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：193 / 199

页数：7

共 50 条

[21] On the Hermitian positive defnite solution of the nonlinear matrix equation X + A*X−1A + B*X−1B = I
Jian-hui Long
Xi-yan Hu
Lei Zhang
Bulletin of the Brazilian Mathematical Society, New Series, 2008, 39 : 371 - 386
[22] Solutions and perturbation analysis for the nonlinear matrix equation X +Σi=1mAi*X-1Ai = I
Duan, Xuefeng
Li, Chunmei
Liao, Anping
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (08) : 4458 - 4466
[23] On equations that are equivalent to the nonlinear matrix equation X plus A*X-α A = Q
Wang, Xing Tao
Li, Yuan Min
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (08) : 2441 - 2449
[24] On the existence of Hermitian positive definite solutions of the matrix equation Xs+A*X-t A=Q
Duan, Xuefeng
Liao, Anping
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (04) : 673 - 687
[25] Some inequalities for the nonlinear matrix equation Xs + A*X-tA = Q: Trace, determinant and eigenvalue
Zhou, Duanmei
Chen, Guoliang
Zhang, Xiangyun
APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 : 21 - 28
[26] An algorithm for computing positive definite solutions of the nonlinear matrix equation X+A*X-1A=I
El-Sayed, S
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2003, 80 (12) : 1527 - 1534
[27] Positive definite solution of the matrix equation X = Q - AX(-1)A
Berzig, Maher
Duan, Xuefeng
Samet, Bessem
MATHEMATICAL SCIENCES, 2012, 6 (01)
[28] On the Hermitian positive definite solution of the nonlinear matrix equation X plus A*X-1A plus B*X-1B = I
Long, Jian-hui
Hu, Xi-yan
Zhang, Lei
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2008, 39 (03): : 371 - 386
[29] A note on positive definite solution of matrix equation X plus M* X-1M - N* X-1N = I
Zhang, Guan-Lin
LINEAR & MULTILINEAR ALGEBRA, 2016, 64 (05) : 951 - 954
[30] Solutions and perturbation estimates for the matrix equation Xs+A*X-tA = Q
Yin, Xiaoyan
Liu, Sanyang
Fang, Liang
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (09) : 1409 - 1421

← 1 2 3 4 5 →