Filtering for Anderson Acceleration
Sara Pollock, Leo G. Rebholz
Abstract
.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 to be particularly effective for problems where the initial iterate may lie far from the solution and which progress through distinct preasymptotic and asymptotic phases.KeywordsAnderson accelerationfilteringconditioningMSC codes65B0565N30