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Anderson mixing (AM) is a classical method that can accelerate fixed-point iterations by exploring historical information. Despite the successful application of AM in scientific computing, the theoretical properties of AM are still under…

Numerical Analysis · Mathematics 2023-07-06 Fuchao Wei , Chenglong Bao , Yang Liu , Guangwen Yang

Anderson acceleration (AA) is widely used for accelerating the convergence of an underlying fixed-point iteration $\bm{x}_{k+1} = \bm{q}( \bm{x}_{k} )$, $k = 0, 1, \ldots$, with $\bm{x}_k \in \mathbb{R}^n$, $\bm{q} \colon \mathbb{R}^n \to…

Numerical Analysis · Mathematics 2025-05-14 Oliver A. Krzysik , Hans De Sterck , Adam Smith

Anderson acceleration (AA) is widely used for accelerating the convergence of nonlinear fixed-point methods $x_{k+1}=q(x_{k})$, $x_k \in \mathbb{R}^n$, but little is known about how to quantify the convergence acceleration provided by AA.…

Numerical Analysis · Mathematics 2023-02-27 Hans De Sterck , Yunhui He , Oliver A. Krzysik

In this paper, we propose a novel Anderson's acceleration method to solve nonlinear equations, which does \emph{not} require a restart strategy to achieve numerical stability. We propose the greedy and random versions of our algorithm.…

Optimization and Control · Mathematics 2024-03-26 Haishan Ye , Dachao Lin , Xiangyu Chang , Zhihua Zhang

Anderson Acceleration (AA) is a popular algorithm designed to enhance the convergence of fixed-point iterations. In this paper, we introduce a variant of AA based on a Truncated Gram-Schmidt process (AATGS) which has a few advantages over…

Numerical Analysis · Mathematics 2024-07-17 Ziyuan Tang , Tianshi Xu , Huan He , Yousef Saad , Yuanzhe Xi

A pervasive approach in scientific computing is to express the solution to a given problem as the limit of a sequence of vectors or other mathematical objects. In many situations these sequences are generated by slowly converging iterative…

Numerical Analysis · Mathematics 2025-07-17 Yousef Saad

We present a convergence theory for Anderson acceleration (AA) applied to perturbed Newton methods (pNMs) for computing roots of nonlinear problems. Two important special cases are the classical Newton method and the Levenberg-Marquardt…

Numerical Analysis · Mathematics 2025-12-03 Matt Dallas

In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and…

Numerical Analysis · Mathematics 2026-02-02 Yunhui He , Santolo Leveque

In this work, we extend a modified Anderson acceleration proposed in [Y. He, arXiv:2603.25983, 2026] to accelerate the Picard iteration for the Navier-Stokes equations. In this variant of Anderson acceleration, named AAg, the nonlinear…

Numerical Analysis · Mathematics 2026-05-19 Yunhui He , Leo Rebholz

This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…

Numerical Analysis · Mathematics 2025-10-21 Nicolas A. Barnafi , Felipe Galarce , Pablo Brubeck

We present a novel two-level sketching extension of the Alternating Anderson-Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multi-physics simulations governed by discretized partial differential…

Numerical Analysis · Mathematics 2026-05-20 Nicolás A. Barnafi , Massimiliano Lupo Pasini

The state-of-art seismic imaging techniques treat inversion tasks such as FWI and LSRTM as PDE-constrained optimization problems. Due to the large-scale nature, gradient-based optimization algorithms are preferred in practice to update the…

Numerical Analysis · Mathematics 2020-11-16 Yunan Yang

This paper applies the Anderson Acceleration (AA) technique to accelerate the Fenchel dual gradient method (FDGM) to solve constrained optimization problems over time-varying networks. AA is originally designed for accelerating fixed-point…

Optimization and Control · Mathematics 2026-01-21 Haijuan Liu , Xuyang Wu

Iterative Closest Point (ICP) is a widely used method for performing scan-matching and registration. Being simple and robust method, it is still computationally expensive and may be challenging to use in real-time applications with limited…

Robotics · Computer Science 2017-09-19 A. L. Pavlov , G. V. Ovchinnikov , D. Yu. Derbyshev , D. Tsetserukou , I. V. Oseledets

We propose an Anderson Acceleration (AA) scheme for the adaptive Expectation-Maximization (EM) algorithm for unsupervised learning a finite mixture model from multivariate data (Figueiredo and Jain 2002). The proposed algorithm is able to…

Machine Learning · Computer Science 2020-09-29 Truong Nguyen , Guangye Chen , Luis Chacon

The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed- point iteration, we explore the use of Anderson…

Numerical Analysis · Mathematics 2016-05-24 Nguyenho Ho , Sarah D. Olson , Homer F. Walker

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for…

Graphics · Computer Science 2018-05-16 Yue Peng , Bailin Deng , Juyong Zhang , Fanyu Geng , Wenjie Qin , Ligang Liu

This paper proposes a new framework for computing low-rank solutions to nonlinear matrix equations arising from spatial discretization of nonlinear partial differential equations: low-rank Anderson acceleration (lrAA). lrAA is an adaptation…

Numerical Analysis · Mathematics 2025-03-25 Daniel Appelo , Yingda Cheng

This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson…

Numerical Analysis · Mathematics 2022-12-09 Sara Pollock , Leo G. Rebholz , Duygu Vargun

Empirical results show that Anderson acceleration (AA) can be a powerful mechanism to improve the asymptotic linear convergence speed of the Alternating Direction Method of Multipliers (ADMM) when ADMM by itself converges linearly. However,…

Optimization and Control · Mathematics 2020-12-01 Dawei Wang , Yunhui He , Hans De Sterck