On inertial iterated Tikhonov methods for solving ill-posed problems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910309858410496 |
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| author | Rabelo, Joel C. Leitão, Antonio Madureira, Alexandre L. |
| author_facet | Rabelo, Joel C. Leitão, Antonio Madureira, Alexandre L. |
| contents | In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We establish convergence for exact data, and stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a 2D Inverse Potential Problem, ii) an Image Deblurring Problem; the computational efficiency of the method is compared with standard implementations of the iT method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On inertial iterated Tikhonov methods for solving ill-posed problems Rabelo, Joel C. Leitão, Antonio Madureira, Alexandre L. Numerical Analysis 65J20, 47J06 In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We establish convergence for exact data, and stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a 2D Inverse Potential Problem, ii) an Image Deblurring Problem; the computational efficiency of the method is compared with standard implementations of the iT method. |
| title | On inertial iterated Tikhonov methods for solving ill-posed problems |
| topic | Numerical Analysis 65J20, 47J06 |
| url | https://arxiv.org/abs/2401.15213 |