Department of Mathematics

Applied Mathematics

  •  Daniel Potts, TU Chemnitz
  •  High dimensional approximation with trigonometric polynomials; zoom link @ https://sites.google.com/view/minds-seminar/home
  •  09/03/2020
  •  2:30 PM - 3:30 PM
  •  

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home) \[ \] In this talk, we present fast Fourier based methods for the approximation of multivariate functions. Our aim is to learn the support of the Fourier coefficients in the frequency domain of high-dimensional functions. We are interested in two different approximation scenarios. The first case is black-box approximation where the user is allowed to sample the unknown function at any point and in the second case we are working with fixed scattered data. For black-box approximation we employ quasi Monte-Carlo methods on rank-1 lattice points. The fast algorithms are then based on one-dimensional fast Fourier transforms (FFT). In the second case, which is much more difficult, we will couple truncated ANOVA (analysis of variance) decompositions with the fast Fourier transform on nonequispaced data (NFFT). In both cases, we present error estimates and numerical results. The presented methods can be understood as sparse high dimensional FFT’s. This talk based on joint work with Lutz Kämmerer, Michael Schmischke, Manfred Tasche, and Toni Volkmer.

 

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