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Numerical Algorithms

, Volume 80, Issue 1, pp 135–234 | Cite as

Comments on “Anderson Acceleration, Mixing and Extrapolation”

  • Donald G. M. AndersonEmail author
Original Paper

Abstract

The Extrapolation Algorithm is a technique devised in 1962 for accelerating the rate of convergence of slowly converging Picard iterations for fixed point problems. Versions to this technique are now called Anderson Acceleration in the applied mathematics community and Anderson Mixing in the physics and chemistry communities, and these are related to several other methods extant in the literature. We seek here to broaden and deepen the conceptual foundations for these methods, and to clarify their relationship to certain iterative methods for root-finding problems. For this purpose, the Extrapolation Algorithm will be reviewed in some detail, and selected papers from the existing literature will be discussed, both from conceptual and implementation perspectives.

Keywords

Fixed point problems Picard iteration Convergence acceleration Anderson Acceleration Anderson Mixing Root-finding problems 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Gordon McKay Professor of Applied Mathematics, EmeritusHarvard John A. Paulson School of Engineering and Applied SciencesCambridgeUSA

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