Some Kinds Of Iterative Algorithms For Large Sparse Linear System

Nowadays, there are a lot of tedious calculation in every branch of mathematics and the fields of engineering technology, which makes computer numerical calculation become more and more important. And an important aspect of numerical calculation is solving large sparse linear systems. Usually, this problem can be solved by the iteration method, it can make use of the sparsity of the matrix to reduce the amount of calculation. So compared with the direct method, the iteration method has more practical applicability and research value. In this paper, it mainly study the iteration methods for singular linear systems, and research a class of iterative algorithms to select the optimal parameters, the results include three parts.Firstly, investigate the generalized parameterized inexact Uzawa(GPIU) methods and give the properties of semi-convergence.Weaking the conditions of the theorem mainly on the basis of previous studies, and present another simple proof.Secondly, the GPIU iteration method is generalized, and proposed amodified GPIU(MGPIU) method for solving singular saddle point problems. The semi-convergence conditions are given, and through the numerical experiments shows that when use the appropriate parameters,the MGPIU method both as a solver and as a preconditioner are very effective.Thirdly, simply summarize the situation for choosing optimal parameters of several types of stationary iterative algorithms, then study the optimal parameters of the unsymmetric SOR-like method(USSOR).Finally, compared the numerical results of SOR-type algorithms by numerical experiments.