The double-step scale splitting method for solving complex Sylvester matrix equation

Abstract

Double-step scale splitting (DSS) approach is an efficient method for a class of large complex symmetric linear systems. In this work, we will apply DSS approach to specify the approximate solution of complex Sylvester matrix equation. We show that the iterative sequence, without any condition, converges to the unique solution of the Sylvester matrix equation, and also we determine the optimal parameter and the corresponding optimal convergence factor. Finally, a test problem is given to illustrate the efficiency of the new technique.