We study the construction and updating of spectral preconditioners for regularized Newton methods and their application to electromagnetic inverse medium scattering problems. Moreover, we show how a Lepski??-type stopping rule can be implemented efficiently for these methods. In numerical examples, the proposed method compares favorably with other iterative regularization method in terms of work-precision diagrams for exact data. For data perturbed by random noise, the Lepski??-type stopping rule performs considerably better than the commonly used discrepancy principle. (Some figures in this article are in colour only in the electronic version)
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