Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916768002342912 |
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| author | Bianchi, Davide Donatelli, Marco Furchì, Davide Reichel, Lothar |
| author_facet | Bianchi, Davide Donatelli, Marco Furchì, Davide Reichel, Lothar |
| contents | The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decomposition to reduce computational complexity by projecting the discretized problem into a lower-dimensional Krylov subspace, in which it is solved. This paper explores the iterated Arnoldi-Tikhonov method, conducting a comprehensive analysis that addresses all approximation errors. Additionally, it introduces a novel strategy for choosing the regularization parameter, leading to more accurate approximate solutions compared to the standard Arnoldi-Tikhonov method. Moreover, the proposed method demonstrates robustness with respect to the regularization parameter, as confirmed by the numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method Bianchi, Davide Donatelli, Marco Furchì, Davide Reichel, Lothar Numerical Analysis 65F22, 47A52 The Arnoldi-Tikhonov method is a well-established regularization technique for solving large-scale ill-posed linear inverse problems. This method leverages the Arnoldi decomposition to reduce computational complexity by projecting the discretized problem into a lower-dimensional Krylov subspace, in which it is solved. This paper explores the iterated Arnoldi-Tikhonov method, conducting a comprehensive analysis that addresses all approximation errors. Additionally, it introduces a novel strategy for choosing the regularization parameter, leading to more accurate approximate solutions compared to the standard Arnoldi-Tikhonov method. Moreover, the proposed method demonstrates robustness with respect to the regularization parameter, as confirmed by the numerical results. |
| title | Convergence analysis and parameter estimation for the iterated Arnoldi-Tikhonov method |
| topic | Numerical Analysis 65F22, 47A52 |
| url | https://arxiv.org/abs/2311.11823 |