Morozov's Discrepancy Principle Under General Source Conditions
- In this paper we study linear ill-posed problems Ax = y in a Hilbert space setting where instead of exact data y noisy data y^delta are given satisfying |y - y^delta| <= delta with known noise level delta. Regularized approximations are obtained by a general regularization scheme where the regularization parameter is chosen from Morozov's discrepancy principle. Assuming the unknown solution belongs to some general source set M we prove that the regularized approximation provides order optimal error bounds on the set M. Our results cover the special case of finitely smoothing operators A and extends recent results for infinitely smoothing operators.
Author: | M. Thamban Nair, Eberhard Schock, Ulrich Tautenhahn |
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URN: | urn:nbn:de:hbz:386-kluedo-12341 |
Series (Serial Number): | Preprints (rote Reihe) des Fachbereich Mathematik (330) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 2002 |
Year of first Publication: | 2002 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2002/08/29 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |