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In this paper, we propose and analyze a set of fully non-stationary Anderson acceleration algorithms with dynamic window sizes and optimized damping. Although Anderson acceleration (AA) has been used for decades to speed up nonlinear…

Numerical Analysis · Mathematics 2022-03-29 Kewang Chen , Cornelis Vuik

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

In this paper, we propose an Anderson-accelerated stochastic extragradient algorithm for solving a class of stochastic variational inequalities, by incorporating Anderson acceleration into the stochastic extragradient method under a…

Optimization and Control · Mathematics 2026-05-27 Xin Qu , Wei Bian , Xiaojun Chen

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

We consider nonlinear convergence acceleration methods for fixed-point iteration $x_{k+1}=q(x_k)$, including Anderson acceleration (AA), nonlinear GMRES (NGMRES), and Nesterov-type acceleration (corresponding to AA with window size one). We…

Optimization and Control · Mathematics 2020-11-10 Hans De Sterck , Yunhui He

In this paper we develop convergence and acceleration theory for Anderson acceleration applied to Newton's method for nonlinear systems in which the Jacobian is singular at a solution. For these problems, the standard Newton algorithm…

Numerical Analysis · Mathematics 2023-10-27 Matt Dallas , Sara Pollock

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

A one-step analysis of Anderson acceleration with general algorithmic depths is presented. The resulting residual bounds within both contractive and noncontractive settings reveal the balance between the contributions from the higher and…

Numerical Analysis · Mathematics 2022-09-08 Sara Pollock , Leo Rebholz

This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for the incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ penalty parameter, and Anderson acceleration (AA) is used to…

Numerical Analysis · Mathematics 2021-10-13 Leo G. Rebholz , Duygu Vargun , Mengying Xiao

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

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

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

The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…

Optimization and Control · Mathematics 2020-06-29 Wenqing Ouyang , Yue Peng , Yuxin Yao , Juyong Zhang , Bailin Deng

The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications,…

Graphics · Computer Science 2019-09-04 Juyong Zhang , Yue Peng , Wenqing Ouyang , Bailin Deng

This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing the fixed point operator associated with the…

Numerical Analysis · Mathematics 2020-04-15 Sara Pollock , Leo G. Rebholz , Mengying Xiao

In this paper, we consider the Anderson acceleration method for solving the contractive fixed point problem, which is nonsmooth in general. We define a class of smoothing functions for the original nonsmooth fixed point mapping, which can…

Optimization and Control · Mathematics 2024-12-11 Zekai Li , Wei Bian

We consider two modifications of the Arrow-Hurwicz (AH) iteration for solving the incompressible steady Navier-Stokes equations for the purpose of accelerating the algorithm: grad-div stabilization, and Anderson acceleration. AH is a…

Numerical Analysis · Mathematics 2022-03-04 Pelin G. Geredeli , Leo G. Rebholz , Duygu Vargun , Ahmed Zytoon

This paper presents the design and development of an Anderson Accelerated Preconditioned Modified Hermitian and Skew-Hermitian Splitting (AA-PMHSS) method for solving complex-symmetric linear systems with application to electromagnetics…

Numerical Analysis · Mathematics 2023-08-02 Måns I. Andersson , Felix Liu , Stefano Markidis

We present a novel approach for accelerating AI performance by leveraging Anderson extrapolation, a vector-to-vector mapping technique based on a window of historical iterations. By identifying the crossover point (Fig. 1) where a mixing…

Machine Learning · Computer Science 2024-12-20 Saleem Abdul Fattah Ahmed Al Dajani , David E. Keyes

Convex-nonconvex (CNC) regularization is a novel paradigm that employs a nonconvex penalty function while maintaining the convexity of the entire objective function. It has been successfully applied to problems in signal processing,…

Optimization and Control · Mathematics 2025-02-21 Qiang Heng , Xiaoqian Liu , Eric C. Chi