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Aicke Hinrichs (Mathematisches Institut, Universität Rostock)
Tractability of multivariate integration - old and new results and open problems
Programm / Abstract:
Multivariate integration is one of the prime examples for complexity studies of high dimensional problems. In this talk we review more or less well-known results for deterministic and randomized algorithms, present some new approaches and look at related open problems. We discuss in some detail positive results on the power of random- ized algorithms, in particular importance sampling. An abstract but nonconstructive approach gives a rather general tractability theorem for integration of functions from reproducing kernel Hilbert spaces. We exhibit cases for which the sampling density for the algorithm can be given explicitly based on certain Sobolev type inequalities. We also discuss negative results in the deterministic setting such as the curse of dimensionality even for some small classes of smooth functions.
Zeit:
am Dienstag den 21. Mai 2013 um 16:00
Ort:
MPI für Mathematik in den Naturwissenschaften Leipzig
Inselstr. 22
04103 Leipzig
Leibniz-Hörsaal (G 10) 3. Etage
eingetragen von Valeria Hünniger(Valeria.Huenniger@mis.mpg.de, 0341 9959 50)