A modified shift-splitting preconditioner for saddle point problems

Recently, Cao, Du and Niu [Shift-splitting preconditioners for saddle point problems, Journal of Computational and Applied Mathematics, 272 (2014) 239-250] introduced a shift splitting preconditioner for saddle point problems. In this paper, we establish a modified shift-splitting preconditioner for solving the large sparse augmented systems of linear equations. Furthermore, the preconditioner is based on a modified shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration, which is a generalization of shift-splitting preconditioners. Finally, numerical examples show the spectrum of the new preconditioned matrix for the different parameters.