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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Metadaten
Author:M. Thamban Nair, Eberhard Schock, Ulrich Tautenhahn
URN (permanent link):urn:nbn:de:hbz:386-kluedo-12341
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (330)
Document Type:Preprint
Language of publication:English
Year of Completion:2002
Year of Publication:2002
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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