Several Iterative Methods For Solving Large Sparse Linear System

With the rapid development of modern science and technology,Large-scale and tedious computing has become a stumbling block to forward all kinds of scientific computing and engineering technology.How to improve the efficiency of calculation has been the forefront of modern scientific research problem.Eventually,these problems are summed up in solving large sparse linear systems bAx(28).This paper mainly studied the several iterative algorithms to solve singular saddle point problem.This paper mainly divided into the following three parts.Firstly,we give the semi-convergence analysis about the parameterized preconditioned HSS method for the singular saddle point problems.Through minimization of iterative matrix quasi-spectral radius to find the optimal parameters.What's more,we illustrate the effectiveness by numerical experiments.Secondly,we introduce a new generalized SOR iteration method to solve the singular saddle point problems,its semi-convergence conditionsand numerical experiments are given.Thirdly,we mainly introduce the Uzawa-AOR method.Based on the Moore-Penrose generalized inverse,we analysis the semi-convergence conditions of Uzawa-AOR and a new generalized SOR method under the generalized stationary iteration,numerical experiments are presented.