A class of preconditioned generalized local PSS iteration methods for non-Hermitian saddle point problems

In this paper, a class of new methods based on the positive-definite and skew-Hermitian splitting scheme, called preconditioned generalized local positive-definite and skew-Hermitian splitting (PGLPSS) methods, are considered to solve non-Hermitian saddle point problems. The convergence properties of the proposed methods are analyzed, which prove that the PGLPSS methods are convergent if the iteration parameters and parameter matrices satisfy appropriate conditions. Some numerical experiments are provided to verify the efficiency of the proposed method, showing the competitiveness and efficiency of this novel method over other testing methods, whether it served as a preconditioned iteration method or as a preconditioner to the Krylov subspace method.