Iterative Algorithms For Saddle Point Problems

This paper mainly studies the algorithms,generalized overrelaxation method and acceler-ated Hermintian and skew-Hermitian splitting method for saddle point problems.By analysis of the iterative schemes their convergence conditions and optimal convergence parameters are given out. based on the results of the convergence analysis of the GSOR method and AHSS method,Chebyshev polynomial acceleration of the GSOR method and AHSS method are then studied and both GSOR-SI method and AHSS-SI method are proposed for solving the saddle point problems,secondly,We apply the GSOR method to the GMRES method,thirdly,A new iterative method with three parameters are given out.The paper consists of four chapters.In chapter 1.The overview is given about the study at present in the world,otherwise,We give some introductions and preliminaries for saddle point problems.In chapter2.We investigate generalized SOR iteration scheme,Both GSOR-SI and GSOR-GMRES are proposed for solving the saddle point problems,In particular,We discuss the choice of parameters.In chapter3.We study the scheme of AHSS iterative method and introduce the AHSS-SI method, accordingly We discuss the choice of parameters.In chapter4.We propose a new iterative method for the saddle point problems,Then we give out general formula of the new method and its convergence analysis,The method consists of three parameters.Finally we report some numerical experiments showing the good behavior of the new algorithms for the saddle point problems.