On the Hermitian positive definite solution and Newton's method for a nonlinear matrix equation

被引：0

作者：

Zhang, Juan ^{[1
]}

Li, Shifeng ^{[1
]}

机构：

[1] Xiangtan Univ, Dept Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2021年 / 69卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Nonlinear matrix equation; Hermitian positive definite solution; Newton's method; convergence analysis;

D O I：

10.1080/03081087.2019.1659222

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, necessary and sufficient conditions for the existence of the Hermitian positive definite solution for a nonlinear matrix equation are derived. Then, a sufficient condition for the existence of the unique Hermitian positive definite solution is presented. Further, we propose to use Newton's method to solve this nonlinear matrix equation with some constraints. In addition, we prove the convergence of Newton's method. Finally, we present some numerical examples to illustrate the effectiveness of the derived results.

引用

页码：2093 / 2114

页数：22

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