ON THE NONLINEAR MATRIX EQUATION X + Σi=1m Ai* X-q Ai = Q(0 < q ≤ 1)

被引：11

作者：

Yin, Xiaoyan ^{[1
]}

Wen, Ruiping ^{[2
]}

Fang, Liang ^{[1
]}

机构：

[1] Xidian Univ, Dept Math, Xian 710071, Peoples R China

[2] Taiyuan Normal Univ, Dept Math, Taiyuan 030012, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2014年 / 51卷 / 03期

基金：

美国国家科学基金会;

关键词：

POSITIVE-DEFINITE SOLUTIONS; PERTURBATION ANALYSIS;

D O I：

10.4134/BKMS.2014.51.3.739

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the nonlinear matrix equation [GRAPHICS] is investigated. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Two iterative methods for the maximal positive definite solution are proposed. A perturbation estimate and an explicit expression for the condition number of the maximal positive definite solution are obtained. The theoretical results are illustrated by numerical examples.

引用

页码：739 / 763

页数：25

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ON THE NONLINEAR MATRIX EQUATION X + Σi=1m Ai* X-q Ai = Q(0 &lt; q ≤ 1)

ON THE NONLINEAR MATRIX EQUATION X + Σi=1m Ai* X-q Ai = Q(0 < q ≤ 1)