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Thu, 29 Aug 2002 00:00:00 +0200Thu, 29 Aug 2002 00:00:00 +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 +0200