On the CRI method for solving Sylvester equation with complex symmetric positive semi-definite 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 the new algorithm converges unconditionally to the unique exact solution of the Sylvester matrix equation. In the end we test the new scheme by solving some numerical examples.