Inexact Newton regularization methods in Hilbert scales

TL;DR

This paper introduces inexact Newton regularization methods tailored for nonlinear inverse problems within Hilbert scales, demonstrating their optimal convergence rates under specific conditions.

Contribution

It proposes a new class of inexact Newton methods in Hilbert scales with proven order optimal convergence rates.

Findings

Methods achieve order optimal convergence

Applicable to nonlinear inverse problems in Hilbert scales

Convergence results depend on certain regularity conditions

Abstract

We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.