Shanks and Anderson-type acceleration techniques for systems of nonlinear equations [preprint]

Preprint date

July 11, 2020

Authors

Claude Brezinski, Stefano Cipolla, Michela Redivo-Zaglia, Yousef Saad (professor)

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 algorithm under a new light and exploits a connection with Quasi-Newton methods, in order to establish local linear convergence results of Anderson-type techniques. The methods are tested on a number of problems, including a few that arise from nonlinear Partial Differential Equations.

Link to full paper

Shanks and Anderson-type acceleration techniques for systems of nonlinear equations

Keywords

numerical analysis