The Study Of Iterative Methods For Saddle Point Problems

With the development of modern science and technology,many engineering research areas,such as fluid mechanics,electromagnetism,optimization problems,the least squares problem,elliptic partial differential equations,etc.,cannot live without the large sparse system of linear equations,so there has been a saddle point problem,of which corresponding solution research undoubtedly has wide application foreground and important practical significance.Based on the theory of traditional iteration,we start from the study of a number of experts and scholars in recent years,according to the actual situation of classical saddle point problem,to get to the Uzawa methods,the SOR methods,the HSS methods,and the Krylov subspace methods which as represented by various iterative systems.Then,with a lot of constant iterative methods of nowadays popularity,combined the idea of HS splitting,we promote the classic saddle point problem solving method to the special saddle point problem solving method.Through the directional research of SOR method,we present a new iteration splitting improvement method,for solving a class of saddle point system which contains an asymmetric block and a class of saddle point system containing a non Hermitian block.Then,a detailed discussion on the method in solving the above two kinds of special saddle point iterative format,convergence analysis and selection of the optimal relaxation parameters.Finally,through a numerical example verifies for different optimal matrix of modified SOR method,the only difference is for the convergence rate,while there is no differences for convergence.So when solving the problem of asymmetric saddle point system or a non Hermitian saddle point system,this method is effective.And under the same calculation accuracy,the modified SOR method for solving the special saddle point problem does good to the conventional method to solve the classical saddle point problem.