On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations

TL;DR

This paper introduces a modified Levenberg-Marquardt method combined with a Kaczmarz strategy to effectively solve nonlinear ill-posed operator equations, demonstrating convergence and stability through numerical tests.

Contribution

It proposes a novel regularization approach integrating Levenberg-Marquardt and Kaczmarz methods for nonlinear ill-posed problems.

Findings

The method is proven to be a convergent regularization technique.

Numerical tests confirm stability and effectiveness in a nonlinear inverse doping problem.

The approach outperforms traditional methods in stability and convergence.

Abstract

In this article a modified Levenberg-Marquardt method coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations is investigated. We show that the proposed method is a convergent regularization method. Numerical tests are presented for a non-linear inverse doping problem based on a bipolar model.