Local Analysis of Inverse Problems: Hölder Stability and Iterative Reconstruction
نویسندگان
چکیده
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 non-linearity conditions, but this analysis is based solely on the Hölder continuity of the inverse mapping. AMS classification scheme numbers: 47J25, 35R30, 65J22 Submitted to: Inverse Problems Local Analysis of Inverse Problems: Hölder Stability and Iterative Reconstruction 2
منابع مشابه
Local Inverse Problems: Hölder Stability and Iterative Reconstruction
We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however, the data space can be an arbitrary Banach space. We study sequences of parameter functions generated by a nonlinear Landweber iteration and conditions under ...
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