A relaxed positive-definite and skew-Hermitian splitting preconditioner for saddle point problems

For saddle point linear system whose coefficient matrix is non-Hermitian of positive definite Hermitian part, Pan et al. (2006) proposed a positive-definite and skew-Hermitian splitting (PSS) preconditioner. In this paper, based on the PSS preconditioner, we present a relaxed positive-definite and skew-Hermitian splitting (RPSS) preconditioner. We analyze the spectral properties of the new preconditioned matrix and conclude that the RPSS preconditioner has much better properties than PSS. Numerical experiments of a model Navier-Stokes problem are presented to illustrate the effectiveness of the new preconditioner.