Three Anderson Accelerated Iterative Methods for Solving Large Scale Linear Equations

Anderson acceleration is a kind of effective method for improving the convergence of the general fixed point iteration. In the linear case, Anderson acceleration can be used to improve the convergence rate of matrix splitting based iterative methods. In this paper, by using Anderson acceleration on general splitting iterative methods for linear systems, three classes of methods are given. The first one is obtained by directly applying Anderson acceleration on splitting iterative methods. For the second class of methods, Anderson acceleration is used periodically in the splitting iteration process. The third one is constructed by combining the Anderson acceleration and split iteration method in each iteration process. The key of this class of method is to determine a combination coefficient for Anderson acceleration and split iteration method. One optimal combination coefficient is given. Some theoretical results about the convergence of the considered three methods are established. Numerical experiments show that the proposed methods are effective.