The parameterized upper and lower triangular splitting methods for saddle point problems

In this paper, we propose a class of parameterized upper and lower triangular splitting (denoted by PULTS) methods for solving nonsingular saddle point problems. The eigenvalues and eigenvectors of iteration matrix of the proposed iteration methods are analyzed. It is shown that the proposed methods converge to the unique solution of linear equations under certain conditions. Besides, the optimal iteration parameters and corresponding convergence factors are obtained with some special cases of the PULTS methods. Numerical experiments are presented to confirm the theoretical results, which implies that PULTS methods are effective and feasible for saddle point problems.