Preliminary list of abstracts

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Infinite-dimensional numerical integration
Keywords: numerical integration; quasi-Monte Carlo; multilevel algorithm
Mon, 11:10--11:35
  • Gnewuch, Michael (Department of Computer Science, Christian-Albrechts-University Kiel, Germany)

In many important applications one has to deal with integration problems for functions of a finite (but a priori unknown) number of variables or of infinitely many variables.

In this talk we want to discuss this type of numerical integration problem for functions in weighted reproducing kernel Hilbert spaces. We present upper and lower bounds for the convergence rates of linear algorihms. The lower bounds are constructive and rely on multilevel schemes and quasi-Monte Carlo integration points. Our upper bounds show that these algorithms obtain in many cases (depending on the considered weights and cost function for function evaluation) the optimal convergence rate.