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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Applied numerical mathematics Jg. 168; S. 251 - 273
Hauptverfasser: Wang, Wenli, Song, Caiqin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.10.2021
Schlagworte:
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-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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