The Study Of Iterative Algorithms For Saddle Point Problems

Saddle point problems arise from many scientific and engineering computations such as fluid dynamics, the finite element method for solving the Navier-Stokes equation, constrained least squares problems, constrained optimization problems and so on. Since the above problems are large and sparse, the iterative methods are effective for saving the storage space and decreasing the computation time, so it is vary important to study of the effective iterative methods for saddle point problems. Recently, many researchers have proposed some effective iterative methods, such as SOR-like method, Uzawa method, GSOR method, MSSOR method and so on. In this paper, we mainly study the iterative methods for saddle point problems and generalized saddle point problems. First, we review the SOR-like method and the MSSOR method, and analysis the convergence and the optimal relaxation parameter. Then we pose the MSOR-like method, analysis its convergence and determine the optimal relaxation parameter under certain condition. Finally, we investigate the MSOR-like method for the generalized saddle point problems, and supply the convergence condition. The numerical example and the theory show that the MSOR-like method’s computational format is simple and has extensive applicability.