A generalized shift-splitting preconditioner for singular saddle point problems

Recently, some authors (Cao et al., 2014; Chen and Ma, 2015; Salkuyeh et al., 2014) discussed the (generalized) shift-splitting preconditioner for nonsingular saddle point problems. In this paper, we further study the generalized shift-splitting preconditioner for solving singular saddle point problems with symmetric positive definite (1, 1)-block. Theoretical analysis shows that the generalized shift-splitting iteration method is unconditionally semi-convergent. Numerical experiments are given to illustrate the efficiency of the proposed preconditioner with appropriate parameters.