The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (232 KB) | Metadata | Table of Contents | ZAA summary
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