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Zeitschrift für Analysis und ihre Anwendungen

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Volume 22, Issue 1, 2003, pp. 199–214
DOI: 10.4171/ZAA/1140

Published online: 2003-03-31

Morozov's Discrepancy Principle under General Source Conditions

M. Thamban Nair[1], E. Schock[2] and Ulrich Tautenhahn

(1) Indian Institute of Technics, Madras, Chennai, India
(2) Universität Kaiserslautern, Germany

We study linear ill-posed problems Ax = y in a Hilbert space setting where instead of exact data y noisy data yd are given satisfying ||y - yd|| ≤ d with known noise level d. 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 extend recent results for infinitely smoothing operators.

Keywords: Linear ill-posed problems, regularization, discrepancy principle, general source conditions, order optimal error bounds

Nair M. Thamban, Schock E., Tautenhahn Ulrich: Morozov's Discrepancy Principle under General Source Conditions. Z. Anal. Anwend. 22 (2003), 199-214. doi: 10.4171/ZAA/1140