Some investigation on Hermitian positive-definite solutions of a nonlinear matrix equation

被引：4

作者：

Pei, Weijuan ^{[1
]}

Wu, Guoxing ^{[1
]}

Zhou, Duanmei ^{[2
]}

Liu, Yitian ^{[1
]}

机构：

[1] Northeast Forestry Univ, Dept Math, Harbin 150040, Peoples R China

[2] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2014年 / 91卷 / 05期

关键词：

nonlinear matrix equation; Hermitian positive-definite solution; necessary and sufficient condition; iteration; SUFFICIENT CONDITIONS; EXISTENCE; X-S+A-ASTERISK-X(-T)A;

D O I：

10.1080/00207160.2013.819425

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 are considered. New necessary and sufficient conditions for the equation to have a Hermitian positive-definite solution are derived. In particular, when A is singular, a new estimate of Hermitian positive-definite solutions is obtained. In the end, based on the fixed point theorem, an iterative algorithm for obtaining the positive-definite solutions of the equation with Q = I is discussed. The error estimations are found.

引用

页码：872 / 880

页数：9

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