Numerische Mathematik

, Volume 72, Issue 1, pp 21–37

A convergence analysis of the Landweber iteration for nonlinear ill-posed problems

  • Martin Hanke
  • Andreas Neubauer
  • Otmar Scherzer

DOI: 10.1007/s002110050158

Cite this article as:
Hanke, M., Neubauer, A. & Scherzer, O. Numer Math (1995) 72: 21. doi:10.1007/s002110050158

Summary.

In this paper we prove that the Landweber iteration is a stable method for solving nonlinear ill-posed problems. For perturbed data with noise level \(\delta \) we propose a stopping rule that yields the convergence rate\(O (\delta ^{1/2}\) ) under appropriate conditions. We illustrate these conditions for a few examples.

Mathematics Subject Classification (1991): 65J15, 65J20, 47H17 

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Martin Hanke
    • 1
  • Andreas Neubauer
    • 1
  • Otmar Scherzer
    • 1
  1. 1.Institut für Mathematik, Johannes-Kepler-Universität, A-4040 Linz, Austria AT

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