Modification on the convergence results of the Sylvester matrix equation AX plus X B = C

In this paper, we investigate some convergence results of the gradient based iterative algorithm for solving the Sylvester matrix equation AX + X B = C. We first review the development of the gradient based iterative algorithm and correct mistakes of some convergence results. Then, the idea of two iterative factors is applied to propose some new relaxed gradient iterative algorithms to improve the convergence performance of their previous algorithms. Finally, some numerical examples are taken to illustrate the correctness of the concluded results. (c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

In this paper, the convergence results of the gradient-based iterative algorithm for solving the Sylvester matrix equation are investigated. New relaxed gradient iterative algorithms are proposed to improve the convergence performance, based on the idea of two iterative factors. Numerical examples are provided to illustrate the correctness of the results.