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arXiv · 2502.05355

Convergence Properties of Nonlinear GMRES Applied to Linear Systems

Chen Greif·Yunhui He
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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.

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Chen Greif, Yunhui He. 2025-02-07. Convergence Properties of Nonlinear GMRES Applied to Linear Systems. https://arxiv.org/abs/2502.05355

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