A new approach for computing the solution of Sylvester matrix equation

Abstract

The aim of this article is modifying the well-known homotopy perturbation method (HPM) to yield the solution of Sylvester matrix equation. Moreover, conditions are deduced to check the convergence of the homotopy series. The numerical implementations will be conducted to measure the accuracy and speed of the homotopy series. Finally, some applications of this linear matrix equation are given.