TY - INPR
A1 - Nair, M. Thamban
A1 - Schock, Eberhard
A1 - Tautenhahn, Ulrich
T1 - Morozov's Discrepancy Principle Under General Source Conditions
N2 - 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.
T3 - Preprints (rote Reihe) des Fachbereich Mathematik - 330
Y1 - 2002
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1343
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-12341
ER -