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arXiv · 2007.05716

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

Claude Brezinski·Stefano Cipolla·Michela Redivo-Zaglia·Yousef Saad
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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.

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Claude Brezinski, Stefano Cipolla, Michela Redivo-Zaglia, Yousef Saad. 2020-07-11. Shanks and Anderson-type acceleration techniques for systems of nonlinear equations. https://arxiv.org/abs/2007.05716

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