TY - INPR
A1 - Pereverzev, Sergei
A1 - Schock, Eberhard
T1 - On the adaptive selection of the parameter in regularization of ill-posed problems
N2 - 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.
T3 - Schriften zur Funktionalanalysis und Geomathematik - 1
KW - Inverse problems in Banach spaces
KW - parameter choice
KW - Abel integral equations
KW - Lavrentiev regularization for equations with monotone operators
Y1 - 2003
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1445
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-12668
ER -