Regularized DPSS preconditioners for non-Hermitian saddle point problems

Based on a new regularized deteriorated positive and skew-Hermitian splitting (RDPSS) of the coefficient matrix, a RDPSS preconditioner is introduced for non-Hermitian saddle point problems. From implementation aspects, the RDPSS preconditioner has better computing efficiency than the regularized Hermitian and skew-Hermitian preconditioner studied recently (Bai and Benzi, 2017). It is proved that the corresponding RDPSS stationary iteration method is convergent unconditionally. In addition, clustering property of the eigenvalues of the RDPSS preconditioned matrix is carefully studied.