A Class Of Numerical Iterative Methods For Solving Large Lin Ear Equations

The numerical solution of the large sparse linear equations is an important subject in the field of thescientific computing and numerical algebra.Due to the large scale of linear system,in the practical application,the iterative method has replaced the direct method and become the most important method for solving large sparse linear equations.So it is significant to study the numerical algorithm and its convergence properties and the convergence rate of the large linear systems.In this paper,it mainly study the iteration methods for solving the large linear systems,perform some theoretical analyses and give the convergence conditions of the iterative methods,then study the choice of the optimal iterative parameters of the iterative algorithm,the paper includes three parts.Firstly,investigate a triple-parameter modified SSOR method and give the properties of semi-convergence,then study the optimal iterative parameters of this method.Finally,compared the numerical results of SOR-type algorithms by numerical experiments and demonstrate the effectiveness of the method.Secondly,add the momentum factors on basis of the SORL method,and propose a SOR momentum acceleration method for solving saddle point problems.The convergence conditions are given,and shows the effectiveness of the method through the numerical experiments.Thirdly,study the fixed parameter with the QCA method for solving the saddle point problem and give the properties of convergence,then analyse the choice of the optimal iterative parameters.