A simplified PSS preconditioner for non-Hermitian generalized saddle point problems

Abstract

The preconditioner for positive-definite and skew-Hermitian splitting (PSS) iteration method has been used to solve saddle point problems. Firstly, we propose a simplified PSS preconditioner for non-Hermitian generalized saddle point problems, which is much closer to original matrix than other PSS preconditioners. Moreover, the spectral properties of preconditioned matrix are also discussed. Finally, we give an example to illustrate the efficiency of the new preconditioner which is used to accelerate the convergence rate of the Krylov subspace, such as GMRES method, it has an obvious advantage than other preconditioners.