The parameterized modified SOR-like method for saddle point problems from Stokes equations *

Abstract Inspired by MSOR-like iteration method proposed by Guo et al. 25 and NMSSOR iteration method proposed by Najafi et al. 32, parameter acceleration technique and preconditioning matrix Q are used, we establish a parameterized modified SOR-like (PMSOR-like) method for non-singular and singular saddle point problems. Theoretical analysis show that the convergence and semi-convergence properties of the PMSOR-like method can be guaranteed under suitable conditions. For nonsingular cases, we give the local theoretical optimal parameters of PMSOR-like method and the corresponding convergence factor. In addition, numerical examples are given to verify the efficiency of the proposed method.