## 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.

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Author: Sergei Pereverzev, Eberhard Schock urn:nbn:de:hbz:386-kluedo-12668 Schriften zur Funktionalanalysis und Geomathematik (1) Preprint English 2003 2003 Technische Universität Kaiserslautern 2003/11/10 Abel integral equations; Inverse problems in Banach spaces; Lavrentiev regularization for equations with monotone operators; parameter choice Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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