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On the adaptive selection of the parameter in regularization of ill-posed problems
- We study a possiblity to use the structure of the regularization error for a posteriori choice of the regularization parameter. As a result, a rather general form of a selection criterion is proposed, and its relation to the heuristical quasi-optimality principle of Tikhonov and Glasko (1964), and to an adaptation scheme proposed in a statistical context by Lepskii (1990), is discussed. The advantages of the proposed criterion are illustrated by using such examples as self-regularization of the trapezoidal rule for noisy Abel-type integral equations, Lavrentiev regularization for non-linear ill-posed problems and an inverse problem of the two-dimensional profile reconstruction.
Author: | Sergei Pereverzev, Eberhard Schock |
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URN: | urn:nbn:de:hbz:386-kluedo-12668 |
Series (Serial Number): | Schriften zur Funktionalanalysis und Geomathematik (1) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 2003 |
Year of first Publication: | 2003 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2003/11/10 |
Tag: | Abel integral equations; Inverse problems in Banach spaces; Lavrentiev regularization for equations with monotone operators; parameter choice |
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 |