A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations

This paper is concerned with a generalization of the Hermitian and skew-Hermitian splitting iteration for solving positive definite, non-Hermitian linear systems. It is shown that the new scheme has some advantages over the standard HSS method, and can be used as an effective preconditioner for certain linear systems in saddle point form. Numerical experiments using discretizations of incompressible flow problems demonstrate the effectiveness of the generalized HSS preconditioner.