Three Anderson Accelerated Iterative Methods for Solving Large Scale Linear Equations (Journal of Computational Mathematics, 2025)
Anderson acceleration is a kind of effective method for improving the convergenceof the general fixed point iteration. In the linear case, Anderson acceleration can beused to improve the convergence rate of matrix splitting based iterative methods. In thispaper, by using Anderson acceleration on general splitting iterative methods for linearsystems, three classes of methods are given. The first one is obtained by directly applyingAnderson acceleration on splitting iterative methods. For the second class of methods,Anderson acceleration is used periodically in the splitting iteration process. The third oneis constructed by combining the Anderson acceleration and split iteration method in eachiteration process. The key of this class of method is to determine a combination coefficientfor Anderson acceleration and split iteration method. One optimal combination coefficientis given. Some theoretical results about the convergence of the considered three methodsare established. Numerical experiments show that the proposed methods are effective.