Anderson加速方法中的松弛参数选取

On choice of relaxation parameter for Anderson acceleration method

Anderson加速方法是提高不动点迭代收敛速度的一类方法。该方法中的松弛参数一般在区间(0,1]内,且大多数选取为1。考虑扩大Anderson加速方法中松弛参数的选取范围,以求解非线性扩散方程的Picard迭代过程为例,比较了不同松弛参数选取方法的效果。数值结果表明,合适的松弛参数可以有效提高Anderson加速方法的效果。

Anderson acceleration method is a kind of method to improve the convergence speed of fixed-point iteration.The relaxation parameter is generally in the interval(0,1],and is selected as 1 in most cases.This paper expanded the selection range of the relaxation parameter.Taking the Picard iteration of solving the nonlinear diffusion equation as an example,the effect of the relaxation parameter selection method was compared.The numerical results show that the appropriate relaxation parameter can effectively improve the convergence speed of the Anderson acceleration method.