nlKrylov: A Unified Framework for Nonlinear GCR-type Krylov Subspace Methods
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917089710702592 |
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| author | Werner, Tom Wan, Ning Miedlar, Agnieszka |
| author_facet | Werner, Tom Wan, Ning Miedlar, Agnieszka |
| contents | In this paper, we introduce a unified framework for nonlinear Krylov subspace methods (nlKrylov) to solve systems of nonlinear equations. Building on classical GCR-like/type linear Krylov solvers such as GMRESR, we generalize these approaches to nonlinear problems via nested algorithmic structures. We present rigorous convergence results for problems, relying on relaxed assumptions that avoid the need for exact line searches. The framework is further extended to matrix-valued rootfinding problems using global nonlinear Krylov approaches. Extensive numerical experiments validate the theoretical insights and demonstrate the robustness and efficiency of our proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14713 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | nlKrylov: A Unified Framework for Nonlinear GCR-type Krylov Subspace Methods Werner, Tom Wan, Ning Miedlar, Agnieszka Numerical Analysis 39B42, 65B99, 65F08, 65F10, 65H10, 65N22, 68W25, 90C53 In this paper, we introduce a unified framework for nonlinear Krylov subspace methods (nlKrylov) to solve systems of nonlinear equations. Building on classical GCR-like/type linear Krylov solvers such as GMRESR, we generalize these approaches to nonlinear problems via nested algorithmic structures. We present rigorous convergence results for problems, relying on relaxed assumptions that avoid the need for exact line searches. The framework is further extended to matrix-valued rootfinding problems using global nonlinear Krylov approaches. Extensive numerical experiments validate the theoretical insights and demonstrate the robustness and efficiency of our proposed algorithms. |
| title | nlKrylov: A Unified Framework for Nonlinear GCR-type Krylov Subspace Methods |
| topic | Numerical Analysis 39B42, 65B99, 65F08, 65F10, 65H10, 65N22, 68W25, 90C53 |
| url | https://arxiv.org/abs/2511.14713 |