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Hein, Torsten : Regularization in Banach spaces - optimal convergence rates results

Hein, Torsten : Regularization in Banach spaces - optimal convergence rates results

Author(s):
Hein, Torsten
Title:
Regularization in Banach spaces - optimal convergence rates results
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 11, 2008
Mathematics Subject Classification:
47A52 [ Ill-posed problems, regularization ]
47J06 [ Nonlinear ill-posed problems ]
49N45 [ Inverse problems ]
Abstract:
In this preprint we deal with convergence rates for a Tikhonov-like regularization approach for linear and non-linear ill-posed problems in Banach spaces. Therefore we deal with so-called distance functions which quantify the violation of a (non-linear) reference source condition. Under validity of this reference source condition we derive convergence rates which are optimal in a Hilbert space situation. In the linear case we additionally present error bounds and convergence rates which base on the decay rate of the distance functions when the reference source condition is violated.
Keywords:
inverse problem, nonlinear ill-posed problem, regularization, Bregman distance, convergence rates
Language:
English
Publication time:
5 / 2008