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Seminar Details

Date 19-4-2006
Time 14:30
Room/Location Sala Conferenze - num 322 - 3° piano
Title Inverse Problems: An analysis of choosing the regularization parameter with respect to stochastical
Speaker Dott. Frank Bauer
Affiliation University of Göttingen
Link http://www.uni-goettingen.de/
Abstract his talk presents research which was in various combinations partly done in collaboration with Sergei Pereverzev (RICAM Linz), Peter Mathe (WIAS Berlin), Thorsten Hohage (Univ. Göttingen), Axel Munk (Univ. Göttingen), Nicolai Bissantz (Univ. Göttingen) and Olha Ivanyshyn (Univ. Göttingen). Inverse problems occur in very many different situations ranging from determining not directly accessible physical quantities out of indirect measurements to approximation/regression to financial models and learning theory with kernel based methods. Due to their instability, one of the major tasks for efficient regularization methods are reliable algorithms for choosing the regularization parameter. This topic became pressing because with new noise models and areas of applications well-known methods like Morozov's balancing principle proved to be not appropriate any more. In this talk a new strategy, the Lepskij type balancing principle is presented. We were able to prove that it yields as good results as the former methods in all classical situations and gives significant improvements in stochastical noise models. Numerics supporting these theoretical considerations will be shown. Parameter choice methods like the balancing principle (but also any other proven one known to me) need the size of the error in one way or another. We will present a way out using a more Baysian approach which could give rise to new methods with much less restrictive requirements on the data; again we will present supporting numerics.
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