Extension of Traub-like methods to regularize nonlinear ill-posed equations in Hilbert scales

Abstract

An extended version of fourth-order Traub-like scheme is applied to approximate nonlinear ill-posed operator equations within the framework of Hilbert scales. A detailed convergence analysis is conducted, yielding an error estimate of optimal order. Furthermore, the adaptive parameter selection strategy proposed by Pereverzev and Schock (2005) is considered for the choice of regularization parameter.