HERMITIAN POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION Xs + A*X-tA = Q

被引：1

作者：

Masoudi, Mohsen ^{[1
]}

Moghadam, Mahmoud Mohseni ^{[1
]}

Salemi, Abbas ^{[1
]}

机构：

[1] Shahid Bahonar Univ Kerman, Dept Math, Kerman, Iran

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2017年 / 54卷 / 06期

关键词：

iterative algoritheorem; nonlinear matrix equation; positive definite solution; fixed point theorem; X-S+A-ASTERISK-X(-T)A; EXISTENCE;

D O I：

10.4134/JKMS.j160429

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Hermitian positive definite solutions of the matrix equation X-s + A*X(-t)A = Q, where Q is an n x n Hermitian positive definite matrix, A is an n x n nonsingular complex matrix and s,t is an element of [1, infinity) are discussed. We find a matrix interval which contains all the Hermitian positive definite solutions of this equation. Also, a necessary and sufficient condition for the existence of these solutions is presented. Iterative methods for obtaining the maximal and minimal Hermitian positive definite solutions are proposed. The theoretical results are illustrated by numerical examples.

引用

页码：1667 / 1682

页数：16

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