Shanks and Anderson-type acceleration techniques for systems of nonlinear equations
Numerical Analysis
2021-07-09 v2 Numerical Analysis
Abstract
This paper examines a number of extrapolation and acceleration methods, and introduces a few modifications of the standard Shanks transformation that deal with general sequences. One of the goals of the paper is to lay out a general framework that encompasses most of the known acceleration strategies. The paper also considers the Anderson Acceleration method under a new light and exploits a connection with quasi-Newton methods, in order to establish local linear convergence results of a stabilized version of Anderson Acceleration method. The methods are tested on a number of problems, including a few that arise from nonlinear Partial Differential Equations.
Keywords
Cite
@article{arxiv.2007.05716,
title = {Shanks and Anderson-type acceleration techniques for systems of nonlinear equations},
author = {Claude Brezinski and Stefano Cipolla and Michela Redivo-Zaglia and Yousef Saad},
journal= {arXiv preprint arXiv:2007.05716},
year = {2021}
}