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

作     者：Wang, Wenli Song, Caiqin 

作者机构：Univ Jinan Sch Math Sci Jinan 250022 Peoples R China Univ Nevada Dept Math & Stat Reno NV 89503 USA 

出 版 物：《APPLIED NUMERICAL MATHEMATICS》 (应用数值数学)

年 卷 期：2021年第168卷

页      面：251-273页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Shandong Natural Science Foundation [2R2020MA052, 2R2020MA055, 2R2017BA010] Anhui Natural Science Foundation [2008085MA12] National Natural Science Foundation of China [11501246, 11801216] 

主　　题：Sylvester discrete-time periodic matrix equations Jacobi iterative algorithm Convergence factor Accelerated Jacobi gradient based iterative algorithm 

摘      要：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 mu 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. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.