Seminar in Numerical Analysis: Jens Oettershagen (Universität Bonn)

Optimal integration in reproducing kernel Hilbert spaces

In this talk, we discuss algorithms for multivariate integration in reproducing kernel Hilbert spaces (RKHS). Here, we study optimally weighted Monte Carlo integration in Sobolev spaces with dominating mixed smoothness. Moreover, we consider integration in spaces of analytic functions. To this end, we construct optimally weighted univariate quadrature rules with carfully selected points and employ them within a generalized sparse grid to the problem of multivariate integration. Applications are given in econometrics and parametric differential equations with affine linear diffusion coefficients.

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