The Equivalent Model Of Saddle Point Problems And Its Preconditioner

Saddle point problems are widely involved in many areas such as fluid dynamics, e-lasticity, electromagnetics, constraint optimization problems and least square problems. Because these problems have so wide application, it is of great interest to develop fast and efficient methods.In this paper, we transformed the saddle point problems into an equivalent model whose coefficient matrix is a symmetric positive definite matrix to solve. Based on SOR iterative method, we construct a Modified accelerative iterative method. The parameter θ of new method is obtained by optimization models other than Chebyshev polynomial. The convergence of the algorithm is also studied. Finally, numerical comparisons are given which show the equivalent model and new accelerative iterative method has faster convergent speed.Second, a new preconditional GMRES method for splitting and iteratively is pro-posed based on large sparse saddle point problems. The spectral radius and best choice of parameter is also studied. Finally, numerical example is given to compare GM-RES method, preconditional HSS method and the new preconditional GMRES method, which show that preconditional GMRES method has higher convergence rate than GM-RES method and the new preconditional GMRES method has higher convergence rate than preconditional HSS method.