Work

Improved Convergence Factor of Windowed Anderson Acceleration for Symmetric Fixed-Point Iterations

Year: 2026

Type: article

Abstract: . This paper studies the commonly utilized windowed Anderson acceleration (AA) algorithm for fixed-point methods, [Formula: see text]. It provides the first proof that when the operator [Formula: see text] is linear, symmetric, and contractive, the windowed AA, which uses a sliding window of prior iterates, improves the root-linear convergence factor over the fixed-point iterations. When [Formula: see text] is nonlinear, yet has a symmetric, non-scalar, and locally contractive Jacobian at a fixed point, a slightly modified AA algorithm is proved to have an analogous root-linear convergence factor improvement over fixed-point iterations. Simulations verify our observations. Furthermore, experiments with different data models demonstrate AA is significantly superior to the standard fixed-point methods for Tyler’s M-estimation.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/24m1643591

Authors: Casey Garner, Gilad Lerman, Teng Zhang

Institutions: University of Minnesota, University of Central Florida

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: ATD:Understanding Adversarial Examples in Neural Network: Theory and Algorithms, Postdoctoral Fellowship: MSPRF: General Matrix Optimization, Mathematically-Guaranteed Global Solutions to Structure-from-Motion, Graduate Research Fellowship Program (GRFP)