On the CRI method for solving Sylvester equation with complex symmetric semi-definite positive coefficient matrices

Abstract

Combination of real and imaginary parts (CRI) method is an efficient method for solving a class of large sparse linear systems with complex symmetric positive semi-definite coefficient matrices. In this work we will extend CRI approach to determine the approximate solution of Sylvester equation with complex symmetric semi-definite positive coefficient matrices. We show that this, without any condition, converges to the unique solution of the Sylvester equation. In the end we test the new scheme by solving a numerical example.