Semi-convergence analysis of parameterized ULT splitting iteration methods for singular saddle point problems

In this paper, we propose the parameterized upper and lower triangular (denoted by PULT) splitting iteration methods for solving singular saddle point problems. The eigenvalues and eigenvectors of iteration matrix of the new methods are studied. It is shown that the proposed methods are semi-convergent under certain conditions. Besides, the pseudo-optimal iteration parameter and corresponding convergence factor can be obtained in some special cases of the PULT iteration methods. Numerical example is presented to confirm the theoretical results, which implies that PULT iteration methods are effective and feasible for solving singular saddle point problems.