JournalszaaVol. 22, No. 1pp. 199–214

Morozov's Discrepancy Principle under General Source Conditions

  • M. Thamban Nair

    Indian Institute of Technics, Madras, Chennai, India
  • Ulrich Tautenhahn

    University of Applied Sciences, Zittau, Germany
  • E. Schock

    Universität Kaiserslautern, Germany
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Abstract

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.

Cite this article

M. Thamban Nair, Ulrich Tautenhahn, E. Schock, Morozov's Discrepancy Principle under General Source Conditions. Z. Anal. Anwend. 22 (2003), no. 1, pp. 199–214

DOI 10.4171/ZAA/1140