Convergence rates of nonlinear inverse problems in Banach spaces: conditional stability and weaker norms

TL;DR

This paper establishes convergence rates for Tikhonov regularization in nonlinear inverse problems within Banach spaces, utilizing conditional stability estimates in weaker norms, and demonstrates applicability to two specific ill-posed inverse problems.

Contribution

It introduces a novel approach using conditional stability in weaker norms to derive convergence rates for nonlinear inverse problems in Banach spaces.

Findings

Convergence rates are derived for Tikhonov regularization in Banach spaces.

The approach applies to two different ill-posed inverse problems.

Conditional stability estimates are key to the analysis.

Abstract

In this short note, we formulate the convergence rates of the well known Tikhonov regularization scheme for solving the nonlinear ill-posed problems in Banach spaces. For deriving the convergence rates, we employ the novel smoothness concept of conditional stability estimates in terms of weaker norms. Moreover, we show that our results are applicable on two ill-posed inverse problems.