ON THE EXTREME SOLUTIONS OF A CLASS OF NONLINEAR MATRIX EQUATION

被引：0

作者：

Meng, Jie ^{[1
]}

Lee, Hosoo ^{[2
]}

Kim, Hyun-Min ^{[1
,3
]}

机构：

[1] Pusan Natl Univ, Finance Fishery Manufacture Ind Math Ctr Big Data, Busan 46241, South Korea

[2] Jeju Natl Univ, Elementary Educ Res Inst, Jeju 63294, South Korea

[3] Pusan Natl Univ, Dept Math, Busan 46241, South Korea

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2020年 / 21卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Nonlinear matrix equation; positive definite solution; cyclic reduction; convergence analysis; POSITIVE-DEFINITE SOLUTIONS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The nonlinear matrix equation X + A*(X) over bar (-1) A = Q, where both the coefficient matrices and the unknown are complex matrices and Q is Hermitian positive definite, is considered. Some new and useful properties of the maximal and minimal positive definite solutions of the matrix equation are obtained. We show that an iteration method with a quadratic convergence rate can be effectively applied to compute the extreme solutions. This iteration method is based on cyclic reduction. Numerical examples and comparisons are provided to show the efficiency of the proposed iteration method.

引用

页码：77 / 87

页数：11

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