Semi-convergence analysis of GMSSOR methods for singular saddle point problems

Abstract

Recently, some authors (Darvishi and Hessari, 2011; Zhang et al., 2012) discussed the generalized modified symmetric successive over relaxation (GMSSOR) method for saddle point problems. In this paper, we further study the GMSSOR method for solving singular saddle point problems. We prove the semi-convergence of the GMSSOR method without the assumption that the (1, 1)-block sub-matrix A should be symmetric, and analyze the spectral property of the corresponding preconditioned matrix. Numerical experiments are given to illustrate the efficiency of GMSSOR with appropriate parameters.