Anderson Acceleration for Fixed-Point Iterations

By Homer F. Walker, Peng Ni. SIAM Journal on Numerical Analysis, 2011

603 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a336b26d37f00182a758acf0156b330b8b73cb27

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In Computational Mechanics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition (2011, methodology): “This reasoning (as in [27]) shows that the nonlinear acceleration mechanism used in N-GMRES is mathematically “essentially equivalent” to GMRES in the linear case (using the terminology of [28]; see also [27, 20, 12, 11]) in the sense that it minimizes the two-norm of the residual over the Krylov sp”
Fast and Robust Iterative Closest Point (2020, methodology): “Anderson acceleration was originally proposed in [37] for iterative solution of nonlinear integral equations, and has proved effective for accelerating fixed-point iterations [8], [38], [39], [40], [41], [42], [43], [44], [45].”
Accelerating Smooth Games by Manipulating Spectral Shapes (2020, methodology): “This is not our concern here, but note that the Green function of G∞ is guaranteed to exist if its boundary is sufficiently nice (see for instance Walsh (1935); Ransford (1995) for a thorough treatment of this classical question).”
Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers (2020, methodology): “The convergence of the iteration may be significantly accelerated by optionally applying Anderson’s method [1, 74].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “Solvers based on Krylov subspace methods [121, 9, 122, 184] and on Anderson relaxation [5, 211, 202] perform intermediate computations in low-dimensional subspaces that are updated as the computation proceeds.”
Numerical Solution of Richards' Equation: A Review of Advances and Challenges (2017, positive): “There has also been renewed interest in acceleration techniques like Anderson acceleration (Walker and Ni, 2011), which can be seen as an approach to improve the quality of Picard (fixed-point) iterates by exploiting the nonlinear residual history using Krylov subspace techniques (Lott et al.”
Physically based modeling in catchment hydrology at 50: Survey and outlook (2015, background): “Along this line, the recent work on Anderson acceleration [Walker and Ni, 2011; Lott et al., 2012] seems promising.”
An assessment of discretizations for convection-dominated convection–diffusion equations (2011, methodology): “Non-linear problems for the SOLD scheme and the FEMTVD scheme were solved by a fixed point iteration with Anderson acceleration [2,41].”
A unified analysis of algebraic flux correction schemes for convection–diffusion equations (2018, methodology): “In [5], the use of the so-called Anderson acceleration, proposed in [3,41], is advocated.”
On the Effectiveness of Richardson Extrapolation in Machine Learning (2020, background): “Acceleration in numerical analysis • Principle – Given asymptotic expansion in t around t∞ (typically 0 or +∞) xt = x∗ + gt +O(ht), where x∗ ∈ R is the desired output and ht = o(‖gt‖) – Combine iterates simply to obtain a sequence yt = x∗ +O(ht) – Without the full knowledge of gt • Linear convergenc”