Accelerated Convergence Iterative Methods Based On The Residual And Its Applications

This paper mainly studies the implementation of iterative method and its ap-plication to accelerate the sequence by sequence transform.Fixed point iteration method is the most common way to solve the coupling problem or nonlinear prob-lems,but its convergence speed is very slow,we construct two acceleration method for sequence transformation based on the residuals,so the convergence speed was improved.Finally through numerical the experiments verify the feasibility and validity of this method.This paper is divided into five chapters:In Chapter 1 it briefly introduces the research background and research status by sequence transform methods to accelerate the convergence of the sequence,and a fixed point iterative methods to accelerate the convergence of Anderson,and vector iteration acceleration method based on the residuals.In Chapter 2 it introduces the general form of accelerated iterative method based on residuals.Based on the difference of the residuals and the number of residuals in the iterative method,the crossed sequences method and alternate sequences method are given in detail.In Chapter 3 it introduces the application of the residual-based acceleration methods in the solution of a class of weakly nonlinear equations and saddle point problems.In Chapter 4 it applies the methods given in this paper to numerical examples.In the first example,we use the methods in this paper to accelerate the Jacobi iteration method and Gauss-Seidel iteration method.In the second case,we obtain the acceleration results of the MHSS algorithm and the Picard-MHSS iteration method.In the third case,the results of the residual-based Uzawa acceleration method for solving the stokes equation is given.In Chapter 5 it we summarize the full thesis and pointed out the further research work.