Comments on “Anderson Acceleration, Mixing and Extrapolation”

Comments on “Anderson Acceleration, Mixing and Extrapolation” Numer Algor https://doi.org/10.1007/s11075-018-0549-4 ORIGINAL PAPER Comments on “Anderson Acceleration, Mixing and Extrapolation” Donald G. M. Anderson Received: 3 May 2018 / Accepted: 10 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The Extrapolation Algorithm is a technique devised in 1962 for acceler- ating 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 1 Introduction In 1962, during the course of my doctoral dissertation research, I devised a technique for accelerating the convergence of the Picard iteration associated with a fixed point problem, which http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Algorithms Springer Journals

Comments on “Anderson Acceleration, Mixing and Extrapolation”

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Computer Science; Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis
ISSN
1017-1398
eISSN
1572-9265
D.O.I.
10.1007/s11075-018-0549-4
Publisher site
See Article on Publisher Site

Abstract

Numer Algor https://doi.org/10.1007/s11075-018-0549-4 ORIGINAL PAPER Comments on “Anderson Acceleration, Mixing and Extrapolation” Donald G. M. Anderson Received: 3 May 2018 / Accepted: 10 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The Extrapolation Algorithm is a technique devised in 1962 for acceler- ating 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 1 Introduction In 1962, during the course of my doctoral dissertation research, I devised a technique for accelerating the convergence of the Picard iteration associated with a fixed point problem, which

Journal

Numerical AlgorithmsSpringer Journals

Published: Jun 5, 2018

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