Convergence Properties of Nonlinear GMRES Applied to Linear Systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915787257675776 |
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| author | Greif, Chen He, Yunhui |
| author_facet | Greif, Chen He, Yunhui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Properties of Nonlinear GMRES Applied to Linear Systems Greif, Chen He, Yunhui Numerical Analysis 65F10, 65F20 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. |
| title | Convergence Properties of Nonlinear GMRES Applied to Linear Systems |
| topic | Numerical Analysis 65F10, 65F20 |
| url | https://arxiv.org/abs/2502.05355 |