Low-triangular Splitting Iteration Method For A Class Of Speclal Generalized Saddle Point Problem

Large-scale Saddle point problems are widely involved in many areas of scientific research and engineering computations, such as constrained and weighted least squares estimation, constrained optimization, computational fluid dynamics, economics, image registration, mixed finite element approximation of elliptic partial differential equations, optimal control and so on. It is interesting to develop fast and efficient methods as these problems have such a wide application source and value.Based on the preconditioned MHSS (PMHSS) method, we construct a lower-triangular splitting (LTS) iteration method scheme for solving a class of block two-by-two linear systems and apply it to the complex linear systems and the distributed control problem. Under suitable restrictions on the iteration parameters, we prove the convergence of the LTS iteration method, moreover determine its optimal iteration parameters and the corre-sponding optimal convergence factor. Numerical implementations show that the resulting of LTS iteration method leads to faster convergence rate than the PMHSS iteration method and Krylov subspace iteration method such as GMRES and its restarted variants, which imply the feasibility of the new iteration method.