22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

Convergence rates for oversmoothing Banach space regularization

23 Sep 2021, 11:30
20m
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt

Speaker

Philip Miller (Institute for Numerical and Applied Mathematics, University of Göttingen, Germany)

Description

We show convergence rates results for Banach space regularization in the case of oversmoothing, i.e. if the penalty term fails to be finite at the unknown solution. We present a flexible approach based on K-interpolation theory which provides more general and complete results than classical variational regularization theory based on various types of source conditions for true solutions contained in the penalty's domain. In particular, we prove order optimal convergence rates for bounded variation regularization. Moreover, we show a result for sparsity promoting wavelet regularization and demonstrate in numerical simulations for a parameter identification problem in a differential equation that our theoretical results correctly predict rates of convergence for piecewise smooth unknown coefficients.

Primary author

Philip Miller (Institute for Numerical and Applied Mathematics, University of Göttingen, Germany)

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