The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation

被引：4

作者：

Zhang, Xindong ^{[1
]}

Feng, Xinlong ^{[2
]}

机构：

[1] Xinjiang Normal Univ, Coll Math Sci, Urumqi 830054, Xinjiang, Peoples R China

[2] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2017年 / 18卷 / 05期

关键词：

Hermitian positive definite solution; nonlinear matrix equation; iterative algorithm; ITERATIVE METHOD; X-S; EXISTENCE; A=I;

D O I：

10.1515/ijnsns-2016-0016

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we study the nonlinear matrix equation X-s +/- Sigma(m)(i=1) A(i)(T) X-delta i A(i) = Q, where A(i) (i = 1,2,..., m) is n x n nonsingular real matrix and Q is n x n Hermitian positive definite matrix. It is shown that the equation has an unique Hermitian positive definite solution under some conditions. Iterative algorithms for obtaining the Hermitian positive definite solution of the equation are proposed. Finally, numerical examples are reported to illustrate the effectiveness of algorithms.

引用

页码：293 / 301

页数：9

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