Convergence Properties of the Single-Step Preconditioned HSS Method for Non-Hermitian Positive Semidefinite Linear Systems

For the nonsingular, non-Hermitian and positive semidefinite linear systems, we derive the convergence results of the single-step preconditioned HSS (SPHSS) method under suitable constraints. Additionally, we consider the acceleration of the SPHSS method by Krylov subspace methods and some spectral properties of the preconditioned matrix are established. Numerical experiments are presented to further examine the effectiveness of the proposed method either as a solver or a preconditioner.