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

Summary.

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.