论文标题
过滤安德森加速
Filtering for Anderson acceleration
论文作者
论文摘要
这项工作介绍，分析并展示了一种有效且理论上的声音过滤策略，以确保在安德森加速的每次迭代中解决最小二乘问题的状况。过滤策略由两个步骤组成：第一个步骤控制最小二乘矩阵列之间的长度差异，第二个是在该矩阵列跨越的子空间之间的角度上执行的下限。证明该组合的策略可以控制每次迭代中最小二乘矩阵的条件数。该方法证明，基于部分微分方程的离散化，该方法对一系列问题有效。对于初始迭代可能远离溶液，并且通过独特的预抑制和渐近阶段进行的问题特别有效。
This work introduces, analyzes and demonstrates an efficient and theoretically sound filtering strategy to ensure the condition of the least-squares problem solved at each iteration of Anderson acceleration. The filtering strategy consists of two steps: the first controls the length disparity between columns of the least-squares matrix, and the second enforces a lower bound on the angles between subspaces spanned by the columns of that matrix. The combined strategy is shown to control the condition number of the least-squares matrix at each iteration. The method is shown to be effective on a range of problems based on discretizations of partial differential equations. It is shown particularly effective for problems where the initial iterate may lie far from the solution, and which progress through distinct preasymptotic and asymptotic phases.
