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Tue, 16 May 2006 13:08:21 +0200Tue, 16 May 2006 13:08:21 +0200Isotone mappings of levelled strict orders
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1736
Strict order relations are defined as strict asymmetric and transitive binary relations. For classes of so-called levelled strict orders it is analyzed, under which conditions the endomorphism monoids of two relations coincide; in particular the case of direct sums of strict antichains is studied. Further, it is shown that these orders differ in their sets of binary order preserving functions.Rainer Lenzpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1736Tue, 16 May 2006 13:08:21 +0200Morozov's Discrepancy Principle Under General Source Conditions
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1343
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.M. Thamban Nair; Eberhard Schock; Ulrich Tautenhahnpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1343Thu, 29 Aug 2002 00:00:00 +0200An economic approach to discretization of nonstationary iterated Tikhonov method
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1277
An adaptive discretization scheme of ill-posed problems is used for nonstationary iterated Tikhonov regularization. It is shown that for some classes of operator equations of the first kind the proposed algorithm is more efficient compared with standard methods.Sergei G. Solodkypreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1277Tue, 05 Feb 2002 00:00:00 +0100