Iterative algorithms for discrete-time periodic Sylvester matrix equations and its application in antilinear periodic system

This paper is dedicated to solving the iterative solution to the discrete-time periodic Sylvester matrix equations. Inspired by Jacobi iterative algorithm and hierarchical identification principle, the Jacobi gradient based iterative (JGI) algorithm and the accelerated Jacobi gradient based iterativ...

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Bibliographic Details
Published in:	Applied numerical mathematics Vol. 168; pp. 251 - 273
Main Authors:	Wang, Wenli, Song, Caiqin
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.10.2021
Subjects:	Accelerated Jacobi gradient based iterative algorithm Convergence factor Jacobi iterative algorithm Sylvester discrete-time periodic matrix equations Sylvester discrete-time periodic matrix equations Jacobi iterative algorithm Accelerated Jacobi gradient based iterative algorithm Convergence factor
ISSN:	0168-9274, 1873-5460
Online Access:	Get full text
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Summary:	This paper is dedicated to solving the iterative solution to the discrete-time periodic Sylvester matrix equations. Inspired by Jacobi iterative algorithm and hierarchical identification principle, the Jacobi gradient based iterative (JGI) algorithm and the accelerated Jacobi gradient based iterative (AJGI) algorithm are proposed. It is verified that the proposed algorithms are convergent for any initial matrix when the parameter factor μ satisfies certain condition. The necessary and sufficient conditions are provided for the presented new algorithms. Moreover, we also apply the JGI algorithm and AJGI algorithm to study a more generalized discrete-time periodic matrix equations and give the convergence conditions of the algorithms. Finally, two numerical examples are given to illustrate the effectiveness, accuracy and superiority of the proposed algorithms.
ISSN:	0168-9274 1873-5460
DOI:	10.1016/j.apnum.2021.06.006