Improved regularizing iterative methods for ill-posed nonlinear systems

TL;DR

This paper develops and analyzes iterative regularization methods for solving nonlinear ill-posed systems, demonstrating their ability to approximate solutions without initial guess proximity, with theoretical and numerical validation.

Contribution

It introduces improved iterative regularization techniques within Levenberg-Marquardt, trust-region, and quadratic regularization frameworks for nonlinear ill-posed problems.

Findings

Methods show regularizing properties theoretically.

Numerical experiments confirm enhanced convergence.

Approach works with both exact and noisy data.

Abstract

In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and noisy data, our focus is on the potential to approach a solution of the unperturbed systems without assumptions on its vicinity to the initial guess. Regularizing properties of the methods proposed are shown theoretically and validated numerically along with enhanced convergence.