Convergence Analysis of Levenberg-Marquardt Method for Inverse Problem with Hölder Stability Estimate
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915104632602624 |
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| author | Ishida, Akari Nagayasu, Sei Nakamura, Gen |
| author_facet | Ishida, Akari Nagayasu, Sei Nakamura, Gen |
| contents | We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy Hölder stability estimate. Furthermore, based on what we found in the mentioned analysis, we develop global reconstruction algorithms for solving inverse problems with finite measurements for exact and noisy data, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of Levenberg-Marquardt Method for Inverse Problem with Hölder Stability Estimate Ishida, Akari Nagayasu, Sei Nakamura, Gen Functional Analysis 47J25, 65J22, 35R30 We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy Hölder stability estimate. Furthermore, based on what we found in the mentioned analysis, we develop global reconstruction algorithms for solving inverse problems with finite measurements for exact and noisy data, respectively. |
| title | Convergence Analysis of Levenberg-Marquardt Method for Inverse Problem with Hölder Stability Estimate |
| topic | Functional Analysis 47J25, 65J22, 35R30 |
| url | https://arxiv.org/abs/2501.08932 |