On normal and skew-Hermitian splitting iteration methods for large sparse continuous Sylvester equations

Abstract

This paper is concerned with some generalizations of the Hermitian and skew-Hermitian splitting (HSS) iteration for solving continuous Sylvester equations. The main contents we will introduce are the normal and skew-Hermitian splitting (NSS) iteration methods for the continuous Sylvester equations. It is shown that the new schemes can outperform the standard HSS method in some situations. Theoretical analysis shows that the NSS methods converge unconditionally to the exact solution of the continuous Sylvester equations. Moreover, we derive the upper bound of the contraction factor of the NSS iterations. Numerical experiments further show the effectiveness of our new methods.