A generalized preconditioned HSS method for singular saddle point problems

Li et al. recently studied the generalized HSS (GHSS) method for solving singular linear systems (see Li et al., J. Comput. Appl. Math. 236, 2338–2353 (2012)). In this paper, we generalize the method and present a generalized preconditioned Hermitian and skew-Hermitian splitting method (GPHSS) to solve singular saddle point problems. We prove the semi-convergence of GPHSS under some conditions, and weaken some semi-convergent conditions of GHSS, moreover, we analyze the spectral properties of the corresponding preconditioned matrix. Numerical experiments are given to illustrate the efficiency of GPHSS method with appropriate parameters both as a solver and as a preconditioner.