On semi-convergence of ULT iterative method for the singular saddle point problems

Zheng and Ma recently proposed an efficient upper and lower triangular (ULT) splitting iterative method for solving the large sparse nonsingular saddle point problems; see Zheng and Ma (2016). In this paper, we further prove the semi-convergence of this method when it is applied to solve the large sparse singular saddle point problems under suitable conditions. The characteristic of eigenvalues of the iteration matrix of the ULT method is analyzed. Also, the pseudo-optimal iteration parameters and the corresponding pseudo-optimal semi-convergence factor for some special cases of the ULT method are determined. In addition, numerical experiments are used to show the feasibility and effectiveness of the ULT iterative method for solving singular saddle point problems.