Investigation of positive definite solution of nonlinear matrix equation Xp = Q+Σmi=1 A*i Xδ Ai

被引：0

作者：

Jin, Zhixiang ^{[1
]}

Zhai, Chengbo ^{[1
]}

机构：

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2021年 / 40卷 / 03期

关键词：

Hermitian positive definite solution; Nonlinear matrix equation; Thompson metric; Perturbation analysis; 15A24; 47H10; EXISTENCE;

D O I：

10.1007/s40314-021-01463-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the nonlinear matrix equation X-p=Q+Sigma(m)(i)=1 A(i)(*)X(delta)A(i), where A(i)(i=1,2,...,m) are n x n nonsingular complex matrices, Q is a n x n Hermitian positive definite (HPD) matrix, p >= 1,m >= 1 are positive integers, and delta is an element of(0,1). We discuss the solution of this equation via properties of Thompson metric and two fixed point theorems in ordered Banach spaces and estimate the bounds of the HPD solution. Furthermore, perturbation analysis is investigated.

引用

页数：14

共 31 条

[1] Al-Dubiban AM, 2015, ABSTR APPL ANAL, V8
[2] [Anonymous], 1985, Matrix Analysis
[3] Bhatia R., 1997, Matrix Analysis, DOI DOI 10.1007/978-1-4612-0653-8
[4] Solution of a class of nonlinear matrix equations
Bose, Snehasish
Hossein, Sk Monowar
Paul, Kallol
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 530 : 109 - 126
[5] Some new bound estimates of the Hermitian positive definite solutions of the nonlinear matrix equation Xs+A*X-tA=Q; [非线性矩阵方程 Xs+A*X-tA=Q的Hermitian正定解的界的新估计]
Cai J.
Chen J.
[J]. Journal of Southeast University (English Edition), 2019, 35 (01) : 142 - 146
[6] Some investigation on Hermitian positive definite solutions of the matrix equation Xs + A*X-tA = Q
Cai, Jing
Chen, Guoliang
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (8-9) : 2448 - 2456
[7] On the existence of Hermitian positive definite solutions of the matrix equation Xs+A*X-t A=Q
Duan, Xuefeng
Liao, Anping
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (04) : 673 - 687
[8] [段雪峰 Duan Xuefeng], 2012, [高等学校计算数学学报, Numerical Mathematics A Journal of Chinese University], V34, P141
[9] On Hermitian positive definite solution of the matrix equation X - Σi=1mAi*XrAi = Q
Duan, Xuefeng
Liao, Anping
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 229 (01) : 27 - 36
[10] ON THE EXISTENCE OF A POSITIVE-DEFINITE SOLUTION OF THE MATRIX EQUATION X=A(T)X(-1)A=I
ENGWERDA, JC
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 194 : 91 - 108

← 1 2 3 4 →