Convergence Analysis of Levenberg-Marquardt Method for Inverse Problem with H\"{o}lder Stability Estimate

TL;DR

This paper analyzes the convergence behavior of the Levenberg-Marquardt method for nonlinear inverse problems with H"{o}lder stability, and develops algorithms for both exact and noisy data scenarios.

Contribution

It provides the first convergence analysis for Levenberg-Marquardt in inverse problems with H"{o}lder stability and introduces global reconstruction algorithms.

Findings

Established local convergence and rates for the method.

Developed global algorithms for finite measurements.

Applicable to both exact and noisy data cases.

Abstract

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 H\"{o}lder 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.