## 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.

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Author: M. Thamban Nair, Eberhard Schock, Ulrich Tautenhahn urn:nbn:de:hbz:386-kluedo-12341 Preprints (rote Reihe) des Fachbereich Mathematik (330) Preprint English 2002 2002 Technische Universität Kaiserslautern 2002/08/29 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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