ON THE EXISTENCE OF POSITIVE DEFINITE SOLUTIONS OF A NONLINEAR MATRIX EQUATION

被引：3
作者：
Li, Jing [1 ]
Zhang, Yuhai [2 ]
机构：
[1] Shandong Univ, Sch Math & Stat, Weihai 264209, Peoples R China
[2] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
来源：
TAIWANESE JOURNAL OF MATHEMATICS | 2014年 / 18卷 / 05期
关键词：
Nonlinear matrix equation; Positive definite solution; Iteration; Perturbation estimate; Backward error; Condition number; Fixed point theorem; PERTURBATION ANALYSIS;
D O I：
10.11650/tjm.18.2014.3747
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper the nonlinear matrix equation X - Sigma(m)(i=1) A(i)* X-pi A(i) = Q with p(i) > 0 is investigated. Necessary and sufficient conditions for the existence of Hermitian positive definite solutions are obtained. An effective iterative method to obtain the unique solution is established. A perturbation bound and the backward error of an approximate solution to this solution is evaluated. Moreover, an explicit expression of the condition number for the positive definite solution is given. The theoretical results are illustrated by numerical examples.
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收藏
页码：1345 / 1364
页数：20
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