Convergence Properties of Nonlinear GMRES Applied to Linear Systems
Numerical Analysis
2026-02-11 v3 Numerical Analysis
Abstract
The Nonlinear GMRES (NGMRES) proposed by Washio and Oosterlee [Electron. Trans. Numer. Anal, 6(271-290), 1997] is an acceleration method for fixed point iterations. It has been demonstrated to be effective, but its convergence properties have not been extensively studied in the literature so far. In this work we aim to close some of this gap, by offering a convergence analysis for NGMRES applied to linear systems. A central part of our analysis focuses on identifying equivalences between NGMRES and the classical Krylov subspace GMRES method.
Cite
@article{arxiv.2502.05355,
title = {Convergence Properties of Nonlinear GMRES Applied to Linear Systems},
author = {Chen Greif and Yunhui He},
journal= {arXiv preprint arXiv:2502.05355},
year = {2026}
}
Comments
23 pages, 2 figures