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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Vydané v:Applied numerical mathematics Ročník 168; s. 251 - 273
Hlavní autori: Wang, Wenli, Song, Caiqin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.10.2021
Predmet:
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
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Popis
Shrnutí: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