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

A modified discrepancy principle to attain optimal rates for polynomially and exponentially ill-posed problems under white noise

23 Sep 2021, 11:10
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt


Tim Jahn


We consider a linear ill-posed equation in the Hilbert space setting under white noise. Known convergence results for the discrepancy principle are either restricted to Hilbert-Schmidt operators (and they require a self-similarity condition for the unknown solution additional to a classical source condition) or to polynomially ill-posed operators (excluding exponentially ill-posed problems). In this work we show optimal convergence for a modified discrepancy principle for both polynomially and exponentially ill-posed operators (without further restrictions) solely under either Hölder-type or logarithmic source conditions. In particular, the method includes only a single simple hyper parameter, which does not need to be adapted to the type of ill-posedness.

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