The Iterative Algorithms For Large Sparse Saddle Point Problems

This paper mainly studies the algorithms,SOR-Like iteration and HSS iteration, for saddle-point problems.By analysis of the iterative schemes their convergence conditions and optimal convergence parameters are given out .Otherwise.we propose a new iterative method for the saddle-point problems in the last chapter. The paper consists of four chapters.In the first chapter we give some introductions and preliminaries for saddle-point problems.In the second chapter we investigate the SOR-Like iterative scheme and its convergence conditions.We study the optimal parameter for the method and make some special choices for Q .In the third chapter we study the scheme of HSS iterative method .We focus on the model problem of Poisson equation and give out the analysis of the choice of the optimal convergence parameter at the continuous level.In the forth chapter we first propose a new iterative method for the saddle-point problems ,then we give out a general formula of the new method and its convergence analysis .One of the two particular formula is proved to have a better convergence condition than the classic Uzawa method.Finally we report some numerical experiments showing the good behavior of the new algorithms for the saddle point problems.