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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

Various statistical tasks, including sampling or computing Wasserstein barycenters, can be reformulated as fixed-point problems for operators on probability distributions. Accelerating standard fixed-point iteration schemes provides a…

Optimization and Control · Mathematics 2026-01-30 Vitalii Aksenov , Martin Eigel , Mathias Oster

Anderson Acceleration (AA) is a method to accelerate the convergence of fixed point iterations for nonlinear, algebraic systems of equations. Due to the requirement of solving a least squares problem at each iteration and a reliance on…

Numerical Analysis · Mathematics 2023-05-08 Shelby Lockhart , David J. Gardner , Carol S. Woodward , Stephen Thomas , Luke N. Olson

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

This paper studies the commonly utilized windowed Anderson acceleration (AA) algorithm for fixed-point methods, $x^{(k+1)}=q(x^{(k)})$. It provides the first proof that when the operator $q$ is linear and symmetric the windowed AA, which…

Numerical Analysis · Mathematics 2025-08-01 Casey Garner , Gilad Lerman , Teng Zhang

Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…

Computation · Statistics 2025-08-19 Nicholas C. Henderson , Ravi Varadhan

We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the…

Numerical Analysis · Mathematics 2024-04-30 Massimiliano Lupo Pasini , M. Paul Laiu

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

Anderson acceleration (AA) is an extrapolation technique designed to speed-up fixed-point iterations like those arising from the iterative training of DL models. Training DL models requires large datasets processed in randomly sampled…

Machine Learning · Computer Science 2021-10-29 Massimiliano Lupo Pasini , Junqi Yin , Viktor Reshniak , Miroslav Stoyanov

Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves…

Numerical Analysis · Mathematics 2024-10-18 Dongdong Liu Ting Hua nd Xifu Liu

Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of…

Optimization and Control · Mathematics 2024-10-16 Kexin Li , Luwei Bai , Xiao Wang , Hao Wang

Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to…

Numerical Analysis · Mathematics 2025-07-15 Xue Feng , M. Paul Laiu , Thomas Strohmer

We address the problem of solving mixed random linear equations. We have unlabeled observations coming from multiple linear regressions, and each observation corresponds to exactly one of the regression models. The goal is to learn the…

Machine Learning · Statistics 2020-08-13 Avishek Ghosh , Kannan Ramchandran

The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…

Optimization and Control · Mathematics 2015-01-16 Hui Zhang , Lizhi Cheng

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

The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the…

Computation · Statistics 2019-06-21 Lucilio Cordero-Grande

Many modern machine learning algorithms such as generative adversarial networks (GANs) and adversarial training can be formulated as minimax optimization. Gradient descent ascent (GDA) is the most commonly used algorithm due to its…

Machine Learning · Computer Science 2022-07-01 Huan He , Shifan Zhao , Yuanzhe Xi , Joyce C Ho , Yousef Saad

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

Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…

Chemical Physics · Physics 2009-11-06 N. Mosyagin , E. Eliav , U. Kaldor

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