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
