Abstract
We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert spaces. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales. Inverse Problems 34(1), 2018, by the same authors. Optimal order convergence rates are established for the specific a priori parameter choice, as used for the corresponding linear equations.
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Acknowledgements
The research was financially supported by Deutsche Forschungsgemeinschaft (DFG-grant HO 1454/12-1) and by the Weierstrass Institute for Applied Analysis and Stochastics, Berlin.
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Hofmann, B., Mathé, P. (2020). A Priori Parameter Choice in Tikhonov Regularization with Oversmoothing Penalty for Non-linear Ill-Posed Problems. In: Cheng, J., Lu, S., Yamamoto, M. (eds) Inverse Problems and Related Topics. ICIP2 2018. Springer Proceedings in Mathematics & Statistics, vol 310. Springer, Singapore. https://doi.org/10.1007/978-981-15-1592-7_8
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DOI: https://doi.org/10.1007/978-981-15-1592-7_8
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