Least squares based iterative algorithm for the coupled Sylvester matrix equations
type: Item
instance of: scholarly article
title: Least squares based iterative algorithm for the coupled Sylvester matrix equations
zbMATH Open document ID: 1407.65048
DOI: 10.1155/2014/831321
author: Hongcai Yin
author: Huamin Zhang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equations \(\mathbf{A} \mathbf{X} + \mathbf{Y} \mathbf{B} = \mathbf{C}\) and \(\mathbf{D} \mathbf{X} + \mathbf{Y} \mathbf{E} = \mathbf{F}\) in this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equation \(\mathbf{A} \mathbf{X} \mathbf{B} + \mathbf{C} \mathbf{X} \mathbf{D} = \mathbf{F}\). The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 7017369
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/831321
OpenAlex ID: W2096402862
Wikidata QID: Q59069721
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description: scientific article; zbMATH DE number 7017369