On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations
Numerical Analysis
2024-06-12 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2406.07044,
title = {On inertial Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations},
author = {Antonio Leitão and Joel C. Rabelo and Dirk A. Lorenz and Maximilian Winkler},
journal= {arXiv preprint arXiv:2406.07044},
year = {2024}
}