On positive-definite and skew-Hermitian splitting iteration methods for continuous Sylvester equation AX+XB=CAX+XB=C

In this paper, we present a positive-definite and skew-Hermitian splitting (PSS) iteration method for continuous Sylvester equations AX+XB=CAX+XB=C with positive definite/semi-definite matrices. The theoretical analysis shows that the PSS iteration method will converge unconditionally and the optimal parameter of the new method is presented. Moreover, to reduce the computing cost, an inexact variant of the PSS iteration method (IPSS) and the analysis of its convergence property in detail have been established. Numerical results show that this new method and its inexact invariant are efficient and robust solvers for this class of continuous Sylvester equations.