An Accelerated Jacobi-gradient Based Iterative Algorithm for Solving Sylvester Matrix Equations

Abstract

In this paper, an accelerated Jacobi-gradient based iterative (AJGI) algorithm for solving
Sylvester matrix equations is presented, which is based on the algorithms proposed by Ding and
Chen [5], Niu et al.[10] and Xie et al.[27]. Theoretical analysis shows that the new algorithm will
converge to the true solution for any initial value under certain assumptions. Finally, several
numerical examples are given to verify the efficiency of the accelerated algorithm.