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SUMMARY:Convergence analysis of the Alternating Anderson-Picard method for nonlinear fixed-point problems (Xue Feng\, UCLA)
DESCRIPTION:Abstract: Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This talk focuses on a variant of AA in which multiple Picard iterations are performed between each AA step\, referred to as the Alternating Anderson-Picard (AAP) method. Despite introducing more `slow’ Picard iterations\, this method has been demonstrated to be efficient and even more robust in both linear and nonlinear cases. However\, there is a lack of theoretical analysis for AAP in the nonlinear context. In this work\, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that employs GMRES to solve a multisecant linear system at each iteration. From this perspective\, we show that AAP actually “converges” the well-known Newton-GMRES method. These connections also help us understand the convergence behavior of AAP\, especially the asymptotic convergence rate.
URL:https://colleges.claremont.edu/ccms/event/convergence-analysis-of-the-alternating-anderson-picard-method-for-nonlinear-fixed-point-problems-xue-feng-ucla/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
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