DOI number:10.1016/j.jfranklin.2022.02.021

Journal:Journal of the Franklin Institute

Key Words:Gradient iterative, Sylvester matrix equation, iterative factor, relaxed gradient iterative, modified gradient iterative

Abstract:In this paper, we investigate some convergence results of the gradient based iterative algorithm for solving the Sylvester matrix equation $AX+XB=C$. 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.

First Author:Zemian Zhang

Indexed by:Journal paper

Correspondence Author:Xuesong Chen

Volume:359

Issue:7

Page Number:3126-3147

Translation or Not:no

Date of Publication:2022-05-01

Included Journals:SCI

Links to published journals:https://doi.org/10.1016/j.jfranklin.2022.02.021