Local analysis of inverse problems: Hölder stability and iterative reconstruction

We consider a class of inverse problems defined by a nonlinear mapping from parameter or model functions to the data, where the inverse mapping is Hölder continuous with respect to appropriate Banach spaces. We analyze a nonlinear Landweber iteration and prove local convergence and convergence rates with respect to an appropriate distance measure. Opposed to the standard analysis of the nonlinear Landweber iteration, we do not assume source and nonlinearity conditions, but this analysis is based solely on the Hölder continuity of the inverse mapping.