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 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.

Automated summary

This paper proposes the Jacobi gradient based iterative (JGI) algorithm and accelerated Jacobi gradient based iterative (AJGI) algorithm for solving the discrete-time periodic Sylvester matrix equations. The algorithms are shown to be convergent for any initial matrix under certain conditions, and their effectiveness and superiority are demonstrated through numerical examples.