ON THE NONLINEAR MATRIX EQUATION <TEX>$X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q$</TEX>(0＜q≤1)

Yin, Xiaoyan; Wen, Ruiping; Fang, Liang

doi:10.4134/BKMS.2014.51.3.739

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ON THE NONLINEAR MATRIX EQUATION ${$X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q$}$ (0＜q≤1)

Journal title : Bulletin of the Korean Mathematical Society
Volume 51, Issue 3, 2014, pp.739-763
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2014.51.3.739

Title & Authors

ON THE NONLINEAR MATRIX EQUATION ${$X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q$}$ (0＜q≤1)
Yin, Xiaoyan; Wen, Ruiping; Fang, Liang;

Abstract

In this paper, the nonlinear matrix equation ${$$X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q(0}$ < ${q{\leq}1)$$}$ is investigated. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Two iterative methods for the maximal positive definite solution are proposed. A perturbation estimate and an explicit expression for the condition number of the maximal positive definite solution are obtained. The theoretical results are illustrated by numerical examples.

Keywords

nonlinear matrix equation;positive definite solution;perturbation estimate;condition number;

Language

English

Cited by

2time(s) in CrossRef

Convergence analysis of some iterative methods for a nonlinear matrix equation, Computers & Mathematics with Applications, 2016, 72, 4, 1164

Positive definite solutions and perturbation analysis of a class of nonlinear matrix equations, Journal of Applied Mathematics and Computing, 2017, 53, 1-2, 245

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