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

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