Solving the nonlinear matrix equation X = Q + Σi=1mMiXδiMi* via a contraction principle

被引：61

作者：

Lim, Yongdo ^{[1
]}

机构：

[1] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 04期

关键词：

Nonlinear matrix equation; Positive definite solution; Thompson metric; Contraction; CONVEXITY;

D O I：

10.1016/j.laa.2008.10.034

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 = Q + Sigma(i=1MiXMi)-M-m-M-delta i* where Q is positive (resp. semidefinite) definite and M-i's are arbitrary (resp. nonsingular) matrices. We prove that if delta:= max(vertical bar delta(i)vertical bar : 1 <= i <= m) < 1. then the equation has a unique positive definite solution which is realized as the unique fixed point of a strict contraction with the Lipschitz constant less than or equal to S. Furthermore, we show that the solution map varying over the determining coefficient matrices is continuous. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1380 / 1383

页数：4

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