Modification on the convergence results of the Sylvester matrix equation [formula omitted].

In this paper, we investigate some convergence results of the gradient based iterative algorithm for solving the Sylvester matrix equation A X + 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. [ABSTRACT FROM AUTHOR]