On saturation of the discrepancy principle for nonlinear Tikhonov regularization in Hilbert spaces

TL;DR

This paper revisits the discrepancy principle for nonlinear Tikhonov regularization in Hilbert spaces, providing improved saturation results under less restrictive conditions compared to previous studies.

Contribution

It introduces new saturation results for the discrepancy principle in nonlinear Tikhonov regularization, relaxing previous restrictive assumptions.

Findings

Enhanced understanding of saturation behavior in nonlinear Tikhonov regularization

Comparison showing improvements over existing saturation results

Broader applicability due to less restrictive conditions

Abstract

In this paper we revisit the discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems in Hilbert spaces and provide some new and improved saturation results under less restrictive conditions, comparing with the existing results in the literature.