Hein, Torsten ; Hofmann, Bernd : Approximate source conditions for nonlinear ill-posed problems - chances and limitations

Author(s):

Hein, Torsten
Hofmann, Bernd

Title:

Approximate source conditions for nonlinear ill-posed problems - chances and limitations

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2008

Mathematics Subject Classification:

47J06			[ Nonlinear ill-posed problems ]
65J20			[ Improperly posed problems; regularization ]
47A52			[ Ill-posed problems, regularization ]

Abstract:

The goal of this paper is to formulate chances and limitations of an application of the method of approximate source conditions, originally developed for linear ill-posed problems in Hilbert spaces in [11], to nonlinear ill-posed problems in reflexive Banach spaces in order to establish convergence rates for a variant of Tikhonov regularization. In this context, we update the concept of (local) degree of nonlinearity from [16] to a Bregman distance setting and extend results from [10] and [13] to alternative situations. In particular, we complement the field of low order convergence rates results in nonlinear regularization theory.

Keywords:

Nonlinear ill-posed problems, regularization, Bregman distance, convergence rates, approximate source conditions, degree of nonlinearity, Banach space, Young's inequality

Language:

English

Publication time:

8 / 2008