Bernd Hofmann
Technische Universität Chemnitz, Germany
Tikhonov regularization with oversmoothing penalty: the interplay between convergence and low order rates
Abstract:
The presentation is devoted to Tikhonov regularization with oversmoothing penalties under conditional stability estimates
for nonlinear ill-posed operator equations in Hilbert scales. Recent results on convergence rates are summarized and
illustrated by numerical case studies. Our focus, however, is on convergence results based on the Banach-Steinhaus theorem.
In this context, it is shown that occurring error estimates can simply be used to derive low order convergence rates in the
oversmoothing case under associated (for example logarithmic) source conditions.
This talk presents joint work with Robert Plato (Siegen), Peter Mathé (Berlin), Daniel Gerth and Christopher Hofmann (Chemnitz).
Research is supported by the Deutsche Forschungsgemeinschaft (DFG) under grant HO 1454/12-1.
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