The iterative methods for solving nonlinear matrix equation X+A⋆X−1A+B⋆X−1B=Q

被引：0

作者：

Sarah Vaezzadeh

Seyyed Mansour Vaezpour

Reza Saadati

Choonkil Park

机构：

[1] Amirkabir University of Technology,Department of Mathematics and Computer Science

[2] Iran University of Science and Technology,Department of Mathematics

[3] Hanyang University,Research Institute for Natural Sciences

来源：

Advances in Difference Equations | / 2013卷

关键词：

nonlinear matrix equation; positive definite solution; inversion-free variant iterative method; convergence rate;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we study the matrix equation X+A⋆X−1A+B⋆X−1B=Q, where A and B are square matrices, and Q is a positive definite matrix, and propose the iterative methods for finding positive definite solutions of the matrix equation. Also, general convergence results for the basic fixed point iteration for these equations are given. Some numerical examples are presented to show the usefulness of the iterations.

引用

共 50 条

[31] The maximal positive definite solution of the nonlinear matrix equation X+A∗X-1A+B∗X-1B=I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X + A^{*}X^{-1}A+B^{*}X^{-1}B = I $$\end{document}
Khosro Sayevand
Raziyeh Erfanifar
Hamid Esmaeili
Mathematical Sciences, 2023, 17 (4) : 337 - 350
[32] Positive definite solution of the matrix equation X = Q - AX(-1)A
Berzig, Maher
Duan, Xuefeng
Samet, Bessem
MATHEMATICAL SCIENCES, 2012, 6 (01)
[33] Perturbation analysis for the positive definite solution of the nonlinear matrix equation X - Sigma(m)(i=1) A(i)(*) X-1 A(i) = Q
Yin, Xiaoyan
Fang, Liang
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2013, 43 (1-2) : 199 - 211
[34] PERTURBATION BOUNDS FOR THE MATRIX EQUATION X plus A*(X)over-cap -1A = Q
Hasanov, Vejdi, I
APPLIED AND COMPUTATIONAL MATHEMATICS, 2020, 19 (01) : 20 - 33
[35] On the nonlinear matrix equation Xs + AHF(X)A = Q
Xie, Yajun
Ma, Changfeng
Zheng, Qingqing
AIMS MATHEMATICS, 2023, 8 (08): : 18392 - 18407
[36] PERTURBATION ANAYSIS FOR THE MATRIX EQUATION X =I - A* X-1
Lee, Hosoo
KOREAN JOURNAL OF MATHEMATICS, 2014, 22 (01): : 123 - 131
[37] 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
[38] Perturbation analysis for the matrix equation X-A*(X)over-cap-1A=Q
Gao, Dongjie
PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON APPLIED MATRIX THEORY, 2009, : 45 - 47
[39] Perturbation Analysis of the Matrix Equation X plus A*X-qA = I(q ≥ 1)
Tang, Bin
Liao, An-Ping
Duan, Xue-Feng
ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL II: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 293 - 296
[40] On Hermitian positive definite solutions of matrix equation X+A*X-2A = I
Zhang, YH
LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 372 : 295 - 304

← 1 2 3 4 5 →