Research And Application Of Anderson Accelerated Algorithm For Solving Large-scale Linear Equations

Anderson acceleration is a kind of effective method to improve the fixed point iteration.In the field of computational chemistry and computational materials science,this method has been successfully applied to many problems.In linear case,Anderson acceleration can be used to improve all kinds of fixed point iterative methods based on matrix splitting,including Jacobi iteration,Gauss-Seidel iteration,etc.With the better parallelism of Anderson acceleration,it is expected to obtain efficient parallel iterative methods for solving large-scale problems with the combination of the fixed point iteration.Based on the Anderson acceleration and the splitting iteration method for solving linear equations,the Anderson accelerated split iteration method is studied in this paper.The main results of this paper are as follows:1.We designed Anderson accelerated split iteration method and Alternating Anderson accelerated split iteration method.These two methods use Anderson acceleration and split iteration to generate iterative points in each iteration.2,Furthermore,we designed hybrid Anderson accelerated splitting iteration method is designed.This kind of method generates iterative points by integrating Anderson acceleration and split iteration in each iteration.The key of this method is to determine the mixing coefficient of Anderson acceleration and splitting iteration.We give the best formula for calculating the mixing coefficient.3.For the above three kinds of iterative methods,a large number of numerical experiments are carried out on three kinds of model problems.The results show that all the three methods are efficient and scalable,in which the Hybrid Anderson accelerated splitting iteration method has faster convergence and higher efficiency than the Anderson accelerated splitting iterative method and the Alternating Anderson accelerated splitting iterative method.