On Landweber iteration for nonlinear ill-posed problems in Hilbert scales

In this paper we derive convergence rates results for Landweber iteration in Hilbert scales in terms of the iteration index \(k\) for exact data and in terms of the noise level \(\delta\) for perturbed data. These results improve the one obtained recently for Landweber iteration for nonlinear ill-posed problems in Hilbert spaces. For numerical computations we have to approximate the nonlinear operator and the infinite-dimensional spaces by finite-dimensional ones. We also give a convergence analysis for this finite-dimensional approximation. The conditions needed to obtain the rates are illustrated for a nonlinear Hammerstein integral equation. Numerical results are presented confirming the theoretical ones.

Authors and Affiliations

1. Institut für Industriemathematik, Johannes-Kepler-Universität, A-4040 Linz, Austria; e-mail: neubauer@indmath.uni-linz.ac.at , , , , , , AT

   Andreas Neubauer

Received May 15, 1998 / Revised version received January 29, 1999 / Published online December 6, 1999

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