A generalized variant of simplified HSS preconditioner for generalized saddle point problems

Abstract

Based on the simplified Hermitian and skew-Hermitian splitting (SHSS) preconditioner developed by Cao, Ren and Shi (BIT Numer. Math., 2016), a generalized variant of the SHSS (GSHSS) preconditioner is presented for solving generalized saddle point problems. The convergence of the GSHSS iteration method and the spectral properties of the preconditioned matrix are studied in details. Eigenvalue bounds and the degree of minimal polynomials of the preconditioned matrix are obtained. In particular, a practical and feasible choice strategy of iteration parameter is given, which also provides a feasible way to select the accelerated parameters for some other preconditioners. Numerical experiments are presented, which show the effectiveness of the proposed preconditioner and the feasibility of the practical choice strategy of accelerated parameter.