On modified HSS iteration methods for continuous Sylvester equations

We introduce and analyze a modification of the Hermitian and skew-Hermitian splitting iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and complex symmetric positive definite/semidefinite matrices. It is found that the modified Hermitian and skew-Hermitian splitting (MHSS) iteration method is unconditionally convergent. Each iteration in this method requires the solution of two linear systems with real symmetric positive definite coefficient matrices. These two systems can be solved inexactly. Numerical results show that the MHSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.