On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911912594243584 |
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| author | Leitão, Antonio Rabelo, Joel C. Lorenz, Dirk A. Winkler, Maximilian |
| author_facet | Leitão, Antonio Rabelo, Joel C. Lorenz, Dirk A. Winkler, Maximilian |
| contents | In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results are: monotonicity and convergence for exact data, stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a parameter identification problem in elliptic PDEs, ii) a parameter identification problem in machine learning; the computational efficiency of the proposed method is compared with canonical implementations of the LM method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_07044 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations Leitão, Antonio Rabelo, Joel C. Lorenz, Dirk A. Winkler, Maximilian Numerical Analysis 65J20, 47J06 In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results are: monotonicity and convergence for exact data, stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a parameter identification problem in elliptic PDEs, ii) a parameter identification problem in machine learning; the computational efficiency of the proposed method is compared with canonical implementations of the LM method. |
| title | On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations |
| topic | Numerical Analysis 65J20, 47J06 |
| url | https://arxiv.org/abs/2406.07044 |