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Anderson

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: 144 Documents
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Cited by 324 Authors

9 Rebholz, Leo Gregory
7 De Sterck, Hans
7 Pollock, Sara
5 John, Volker
5 Kelley, Carl T.
5 Xiao, Mengying
4 Chacón, Luis
4 He, Yunhui
4 Kuzmin, Dmitri
4 Tchelepi, Hamdi A.
3 Brezinski, Claude
3 Chen, Guangye
3 Hauck, Cory D.
3 Jiang, Jiamin
3 Li, Zhizhi
3 Martínez, José Mario
3 Radu, Florin Adrian
3 Redivo-Zaglia, Michela
3 Taitano, William T.
3 Tomin, Pavel
3 Toth, Alex
3 Vargun, Duygu
3 Walker, Homer F.
3 Zhang, Huai
2 An, Hengbin
2 Barrenechea, Gabriel R.
2 Birgin, Ernesto G.
2 Both, Jakub Wiktor
2 Boyd, Stephen Poythress
2 Chen, Kewang
2 Chen, Xiaojun
2 Ciaramella, Gabriele
2 Dede’, Luca
2 Hamilton, Steven P.
2 Huang, Ting-Zhu
2 Knobloch, Petr
2 Knoll, Dana A.
2 Levitt, Antoine
2 Liu, Qinghuo
2 Luo, Songting
2 Milzarek, Andre
2 Nordbotten, Jan Martin
2 Ou-Yang, Le
2 Ouyang, Wenqing
2 Pallavicini, Andrea
2 Pawlowski, Roger P.
2 Quarteroni, Alfio M.
2 Saad, Yousef
2 Scheufele, Klaudius
2 Schulte, Miriam
2 Tyrtyshnikov, Evgeniĭ Evgen’evich
2 Vergara, Christian
2 Vuik, Cornelis
2 Zhang, Junzi
1 Akian, Marianne
1 Al Nazer, Safaa
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1 Ammosov, Dmitry A.
1 Amos, Brandon D.
1 Anderson, Donald G. M.
1 Anderson, Sarah E.
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1 Bai, Zhaojun
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1 Barnafi Wittwer, Nicolás Alejandro
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1 Basting, Christopher
1 Basting, Steffen
1 Beik, Fatemeh Panjeh Ali
1 Benzi, Michele
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1 Berrill, Mark A.
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1 Bochev, M. A.
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1 Brune, Peter R.
1 Bruss, Don E.
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1 Cabrales, Roberto Carlos
1 Cai, Yunfeng
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1 Carpio, Jaime
1 Castillo, Ernesto
1 Catabriga, Lucia
1 Chehab, Jean-Paul
1 Chen, Shi
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Cited in 54 Serials

20 Journal of Computational Physics
12 SIAM Journal on Scientific Computing
11 Computer Methods in Applied Mechanics and Engineering
9 Journal of Computational and Applied Mathematics
8 Numerical Algorithms
7 SIAM Journal on Numerical Analysis
6 Computers & Mathematics with Applications
5 SIAM Journal on Matrix Analysis and Applications
5 Journal of Scientific Computing
3 Applied Mathematics and Computation
3 SIAM Review
3 SIAM Journal on Optimization
3 Computational Geosciences
2 Computers and Fluids
2 Linear Algebra and its Applications
2 Computational Optimization and Applications
2 Numerical Linear Algebra with Applications
2 Advances in Computational Mathematics
2 Communications in Computational Physics
1 Acta Mechanica
1 Archive for Rational Mechanics and Analysis
1 Inverse Problems
1 Mathematics of Computation
1 Applied Mathematics and Optimization
1 Computer Aided Geometric Design
1 Journal of Integral Equations and Applications
1 European Journal of Applied Mathematics
1 Applied Mathematical Modelling
1 SIAM Journal on Applied Mathematics
1 Mathematical Programming. Series A. Series B
1 Journal of Inverse and Ill-Posed Problems
1 ETNA. Electronic Transactions on Numerical Analysis
1 Mathematical and Computer Modelling of Dynamical Systems
1 International Journal of Theoretical and Applied Finance
1 Acta Mathematica Sinica. English Series
1 Differential Equations
1 Quantitative Finance
1 Journal of Systems Science and Complexity
1 Journal of Numerical Mathematics
1 Journal of Applied Mathematics and Computing
1 Multiscale Modeling & Simulation
1 Acta Numerica
1 International Journal of Numerical Analysis and Modeling
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
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1 SIAM Journal on Imaging Sciences
1 Foundations and Trends in Machine Learning
1 Advances in Applied Mathematics and Mechanics
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1 S\(\vec{\text{e}}\)MA Journal
1 Journal of Applied Analysis and Computation
1 SMAI Journal of Computational Mathematics
1 Results in Applied Mathematics
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