swMATH ID: 15192
Software Authors: Homer F. Walker; Peng Ni
Description: Anderson Acceleration for Fixed-Point Iterations. This paper concerns an acceleration method for fixed-point iterations that originated in work of D. G. Anderson [J. Assoc. Comput. Mach., 12 (1965), pp. 547–560], which we accordingly call Anderson acceleration here. This method has enjoyed considerable success and wide usage in electronic structure computations, where it is known as Anderson mixing; however, it seems to have been untried or underexploited in many other important applications. Moreover, while other acceleration methods have been extensively studied by the mathematics and numerical analysis communities, this method has received relatively little attention from these communities over the years. A recent paper by H. Fang and Y. Saad [Numer. Linear Algebra Appl., 16 (2009), pp. 197–221] has clarified a remarkable relationship of Anderson acceleration to quasi-Newton (secant updating) methods and extended it to define a broader Anderson family of acceleration methods. In this paper, our goals are to shed additional light on Anderson acceleration and to draw further attention to its usefulness as a general tool. We first show that, on linear problems, Anderson acceleration without truncation is “essentially equivalent” in a certain sense to the generalized minimal residual (GMRES) method. We also show that the Type 1 variant in the Fang–Saad Anderson family is similarly essentially equivalent to the Arnoldi (full orthogonalization) method. We then discuss practical considerations for implementing Anderson acceleration and illustrate its performance through numerical experiments involving a variety of applications.
Homepage: http://epubs.siam.org/doi/abs/10.1137/10078356X
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Cited in: 108 Publications
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Cited by 257 Authors

5 De Sterck, Hans
5 John, Volker
5 Kelley, Carl T.
5 Pollock, Sara
5 Rebholz, Leo G.
4 Kuzmin, Dmitri
4 Xiao, Mengying
3 Brezinski, Claude
3 Chacón, Luis
3 Hauck, Cory D.
3 Radu, Florin Adrian
3 Redivo-Zaglia, Michela
3 Taitano, William T.
3 Tchelepi, Hamdi A.
3 Toth, Alex
3 Walker, Homer F.
2 An, Hengbin
2 Barrenechea, Gabriel R.
2 Both, Jakub Wiktor
2 Boyd, Stephen Poythress
2 Chen, Guangye
2 Ciaramella, Gabriele
2 Hamilton, Steven P.
2 He, Yunhui
2 Huang, Ting-Zhu
2 Jiang, Jiamin
2 Knobloch, Petr
2 Knoll, Dana A.
2 Levitt, Antoine
2 Li, Zhizhi
2 Martínez, José Mario
2 Nordbotten, Jan Martin
2 Pallavicini, Andrea
2 Pawlowski, Roger P.
2 Scheufele, Klaudius
2 Schulte, Miriam
2 Tomin, Pavel
2 Tyrtyshnikov, Evgeniĭ Evgen’evich
2 Zhang, Huai
2 Zhang, Junzi
1 Akian, Marianne
1 Al Nazer, Safaa
1 Almeida, Regina C.
1 Alpak, Faruk O.
1 Anderson, Donald G. M.
1 Anderson, Sarah E.
1 Appelö, Daniel
1 Araya-Polo, Mauricio
1 Augustin, Matthias Albert
1 Bai, Zhaojun
1 Bakurskiy, S. V.
1 Barnafi Wittwer, Nicolás Alejandro
1 Barnafi, Nicolás A.
1 Basting, Christopher
1 Basting, Steffen
1 Beik, Fatemeh Panjeh Ali
1 Benzi, Michele
1 Bermejo, Rodolfo
1 Berndt, Markus
1 Berrill, Mark A.
1 Bijl, Hester
1 Bindel, David S.
1 Birgin, Ernesto G.
1 Blom, David S.
1 Bochev, M. A.
1 Böhlke, Thomas
1 Bormetti, Giacomo
1 Brune, Peter R.
1 Bruss, Don E.
1 Bungartz, Hans-Joachim
1 Cai, Yunfeng
1 Caiazzo, Alfonso
1 Callegaro, Giorgia
1 Carlson, Neil N.
1 Carpentieri, Bruno
1 Carpio, Jaime
1 Catabriga, Lucia
1 Chehab, Jean-Paul
1 Chen, Xiaojun
1 Chen, Zheng
1 Cheng, Jian
1 Chu, Risheng
1 Chupin, Maxime
1 Clarno, Kevin T.
1 Colera, Manuel
1 Coutinho, Alvaro L. G. A.
1 DeCaria, Victor P.
1 Deckelnick, Klaus
1 Dede’, Luca
1 Di Gregorio, Simone
1 Dolejší, Vít
1 Dupuy, Mi-Song
1 Ellis, J. Austin
1 Ernesti, Felix
1 Evans, Claire
1 Evans, Thomas M.
1 Evans, Tom
1 Fabrini, Giulia
1 Fiebach, André
1 Forbes, Dominique
...and 157 more Authors
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16 Journal of Computational Physics
11 SIAM Journal on Scientific Computing
8 Numerical Algorithms
7 Computer Methods in Applied Mechanics and Engineering
6 Computers & Mathematics with Applications
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5 SIAM Journal on Numerical Analysis
3 SIAM Review
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2 SIAM Journal on Matrix Analysis and Applications
2 SIAM Journal on Optimization
2 Numerical Linear Algebra with Applications
1 Acta Mechanica
1 Archive for Rational Mechanics and Analysis
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1 Mathematics of Computation
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1 Advances in Applied Mathematics and Mechanics
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