On thematrix equation X + AX-1A-BX-1B = I

被引：4

作者：

Hasanov, Vejdi Ismailov ^{[1
]}

机构：

[1] Konstantin Preslavsky Univ Shumen, Fac Math & Informat, Shumen, Bulgaria

来源：

LINEAR & MULTILINEAR ALGEBRA | 2018年 / 66卷 / 09期

关键词：

Nonlinear matrix equation; positive definite solution; iterative method; POSITIVE-DEFINITE SOLUTION; SUFFICIENT CONDITIONS; EXTREME SOLUTIONS; MATRIX; EXISTENCE;

D O I：

10.1080/03081087.2017.1373730

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate the matrix equation X + A * X -1A B * X -1B = I. Some sufficient and necessary conditions for the existence of Hermitian positive definite solutions as well as for the existence of the smallest Hermitian positive definite solution of the considered equation are derived. Two iterative methods for computing the smallest positive definite solution are proposed. Some numerical examples are presented to illustrate the theoretical results.

引用

页码：1783 / 1798

页数：16

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On thematrix equation X + A*X-1A-B*X-1B = I

On thematrix equation X + AX-1A-BX-1B = I