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| Autors principals: | , |
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| Format: | Preprint |
| Publicat: |
2024
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2404.08321 |
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| _version_ | 1866909697642070016 |
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| author | Donatelli, Marco Furchì, Davide |
| author_facet | Donatelli, Marco Furchì, Davide |
| contents | The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the discretized problem into a lower-dimensional Krylov subspace, where the problem is then solved.
This paper studies iAT under an additional hypothesis on the discretized operator. It presents a theoretical analysis of the approximation errors, leading to an a posteriori rule for choosing the regularization parameter. Our proposed rule results in more accurate computed approximate solutions compared to the a posteriori rule recently proposed in arXiv:2311.11823. The numerical results confirm the theoretical analysis, providing accurate computed solutions even when the new assumption is not satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08321 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved parameter selection strategy for the iterated Arnoldi-Tikhonov method Donatelli, Marco Furchì, Davide Numerical Analysis The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the discretized problem into a lower-dimensional Krylov subspace, where the problem is then solved. This paper studies iAT under an additional hypothesis on the discretized operator. It presents a theoretical analysis of the approximation errors, leading to an a posteriori rule for choosing the regularization parameter. Our proposed rule results in more accurate computed approximate solutions compared to the a posteriori rule recently proposed in arXiv:2311.11823. The numerical results confirm the theoretical analysis, providing accurate computed solutions even when the new assumption is not satisfied. |
| title | Improved parameter selection strategy for the iterated Arnoldi-Tikhonov method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.08321 |