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...
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| Vydáno v: | SIAM journal on numerical analysis Ročník 49; číslo 3/4; s. 1715 - 1735 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.01.2011
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| Témata: | |
| ISSN: | 0036-1429, 1095-7170 |
| On-line přístup: | Získat plný text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | WALKER, HOMER F. NI, PENG |
| Author_xml | – sequence: 1 givenname: HOMER F. surname: WALKER fullname: WALKER, HOMER F. – sequence: 2 givenname: PENG surname: NI fullname: NI, PENG |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24618058$$DView record in Pascal Francis |
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| CODEN | SJNAEQ |
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| Cites_doi | 10.1137/S1064827596303843 10.1002/jcc.540030413 10.1016/0009-2614(80)80396-4 10.1016/0927-0256(96)00008-0 10.1111/j.2517-6161.1977.tb01600.x 10.1007/s002110050110 10.1137/1026034 10.1090/S0025-5718-1965-0198670-6 10.1016/S0377-0427(00)00357-5 10.1016/j.patcog.2007.09.010 10.1145/1499096.1499099 10.1137/S106482750037620X 10.1016/S0377-0427(00)00360-5 10.1137/S1064827598338093 10.1137/S1064827502416344 10.1145/321296.321305 10.1137/0718067 10.1137/0907058 10.1016/0024-3795(89)90719-2 10.1016/j.cam.2004.12.032 10.1137/1029042 10.1002/nla.617 10.1016/j.jcp.2003.08.010 10.1103/PhysRevB.54.11169 10.1137/0912003 10.1137/0906055 10.1017/S096249290400025X 10.1137/1021091 10.1137/S106482759426955X 10.1006/jcph.1996.0059 10.1090/S0025-5718-1981-0616364-6 10.1137/S106482759732678X 10.1016/0377-0427(91)90018-F |
| ContentType | Journal Article |
| Copyright | Copyright ©2011 Society for Industrial and Applied Mathematics 2015 INIST-CNRS [Copyright] © 2011 Society for Industrial and Applied Mathematics |
| Copyright_xml | – notice: Copyright ©2011 Society for Industrial and Applied Mathematics – notice: 2015 INIST-CNRS – notice: [Copyright] © 2011 Society for Industrial and Applied Mathematics |
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| Keywords | Orthogonal matrix iterative methods Arnoldi method Decomposition method Iterative method Iteration Numerical method Stochastic method Partial differential equation Truncation Fix point 65F10 Multigrid Least squares method mixture densities 65H10 acceleration methods Arnoldi (full orthogonalization) method expectation-maximization algorithm Quasi Newton method Numerical linear algebra Initial value problem fixed-point iterations Algorithm nonnegative matrix factorization GMRES method Numerical analysis Boundary value problem Linear system Linear algebra Abstract space alternating least-squares generalized minimal residual method Domain decomposition |
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| References | R40 R21 R20 R42 R23 R45 R25 R24 R27 R29 R28 R1 Dempster A. P. (R12) 1977; 39 R2 R3 Washio T. (R43) 1997; 6 R5 R6 R7 R8 Sherman J. (R41) 1949; 20 R30 R10 R34 R11 R33 R36 R13 R35 R16 R38 R15 R37 R18 R19 |
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| Snippet | 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.... |
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| SubjectTerms | Algebra Algorithms Applied mathematics Cost efficiency Exact sciences and technology Experiments Global analysis, analysis on manifolds Iterative solutions Jacobians Linear algebra Linear and multilinear algebra, matrix theory Linear systems Mathematical extrapolation Mathematical vectors Mathematics Matrices Methods Numerical analysis Numerical analysis in abstract spaces Numerical analysis. Scientific computation Numerical methods in probability and statistics Sciences and techniques of general use Secant function Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Truncation |
| Title | ANDERSON ACCELERATION FOR FIXED-POINT ITERATIONS |
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