Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (232 KB) | Metadata | Table of Contents | ZAA summary
Published online: 2003-03-31
Morozov's Discrepancy Principle under General Source ConditionsM. Thamban Nair, E. Schock 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