Abstract
In this paper we study some regularization methods to reconstruct the solution q* of the non-linear ill-posed problem A (q)=z from noisy data zdelta in Z where A:D(A) contained in/implied by Q to Z is a non-linear operator between Hilbert spaces Q and Z. The considered regularization methods are (1) the method of Tikhonov regularization in Hilbert scales, (2) the method of regularization in state space which recently has been proposed by Chavent and Kunisch (1992) and (3) some new regularization methods that are based on data smoothing. Assuming certain conditions concerning the non-linear operator A and the smoothness of the solution q* we discuss a priori as well as a posteriori parameter choice strategies that yield regularized solutions with order optimal error bounds.