Iterative algorithm for solving a system of nonlinear matrix equations
type: Item
instance of: scholarly article
title: Iterative algorithm for solving a system of nonlinear matrix equations
zbMATH Open document ID: 1268.65058
DOI: 10.1155/2012/461407
author: Asmaa M. Al-Dubiban
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: We discuss the positive definite solutions for the system of nonlinear matrix equations \(X - A^\ast Y^{-n} A = I\) and \(Y - B^\ast X^{\-m} B = I\), where \(n, m\) are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive definite solutions are given. An iterative algorithm for obtaining positive definite solutions of the system is proposed. Moreover, the error estimations are found. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6169911
zbMATH Keywords: positive definite solutions
zbMATH Keywords: system of nonlinear matrix equations
zbMATH Keywords: iterative algorithm
zbMATH Keywords: error estimation
zbMATH Keywords: numerical example
Wikidata QID: Q58905916
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/461407
OpenAlex ID: W2104644112
cites work: Q4850020
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DBLP publication ID: journals/jam/Al-Dubiban12
description: scientific article; zbMATH DE number 6169911