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 Lipschitz/Hölder continuous. We perform convergence analysis on a class of iterative reconstruction methods 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 Lipschitz/Hölder continuity of the inverse mapping. A scaled relative graph approach is employed. With this new 2D geometric tool for convergence analysis, we improve the convergence results in a Hilbert space setting.

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