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

In this paper we derive convergence rates results for Landweber iteration i n Hilbert scales in terms of the iteration index k for exact data and in te rms of the noise level delta for perturbed data. These results improve the one obtained recently for Landweber iteration for nonlinear ill-posed probl ems in Hilbert spaces. For numerical computations we have to approximate th e nonlinear operator and the infinite-dimensional spaces by finite-dimensio nal ones. We also give a convergence analysis for this finite-dimensional a pproximation. The conditions needed to obtain the rates are illustrated for a nonlinear Hammerstein integral equation. Numerical results are presented confirming the theoretical ones. Mathematics Subject Classification (1991) : 65J15, 65J20, 47H17.