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

Claude Brezinski, Stefano Cipolla, Michela Redivo-Zaglia, Yousef Saad

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 (AA) 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 the AA method. The methods are tested on a number of problems, including a few that arise from nonlinear partial differential equations.

Original languageEnglish (US)
Pages (from-to)3058-3093
Number of pages36
JournalIMA Journal of Numerical Analysis
Issue number4
StatePublished - Oct 1 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© The Author(s) 2021.


  • Anderson acceleration
  • Krylov subspace methods
  • Navier–Stokes equation
  • extrapolation methods
  • nonlinear Poisson problems
  • quasi-Newton methods
  • regularization


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