Bibliographic Details
| Title: |
On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations |
| Authors: |
Leitão, Antonio, Rabelo, Joel C., Lorenz, Dirk A., Winkler, Maximilian |
| Publication Year: |
2024 |
| Collection: |
Computer Science
Mathematics |
| Subject Terms: |
Mathematics - Numerical Analysis, 65J20, 47J06 |
| More Details: |
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. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2406.07044 |
| Accession Number: |
edsarx.2406.07044 |
| Database: |
arXiv |
