Iterative solutions of a set of matrix equations by using the hierarchical identification principle
type: Item
instance of: scholarly article
title: Iterative solutions of a set of matrix equations by using the hierarchical identification principle
zbMATH Open document ID: 1468.65038
DOI: 10.1155/2014/649524
author: Huamin Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper is concerned with iterative solution to a class of the real coupled matrix equations. By using the hierarchical identification principle, a gradient-based iterative algorithm is constructed to solve the real coupled matrix equations \(A_1 X B_1 + A_2 X B_2 = F_1\) and \(C_1 X D_1 + C_2 X D_2 = F_2\). The range of the convergence factor is derived to guarantee that the iterative algorithm is convergent for any initial value. The analysis indicates that if the coupled matrix equations have a unique solution, then the iterative solution converges fast to the exact one for any initial value under proper conditions. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.
Mathematics Subject Classification ID: 65F45
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 7022826
Wikidata QID: Q59040361
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/649524
OpenAlex ID: W1992181637
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description: scientific article; zbMATH DE number 7022826