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Interpolation lattices for hyperbolic cross trigonometric polynomials
Thu, 11:35--12:00
  • Kämmerer, Lutz (Faculty of Mathematics, Chemnitz University of Technology, Germany)
  • Kunis, Stefan (Osnabrück University, Germany)
  • Potts, Daniel (Chemnitz University of Technology, Germany)

A straightforward discretisation of high dimensional problems often leads to an exponential growth in the number of degrees of freedom. So, computational costs of even efficient algorithms like the fast Fourier transform increase similar.

Trigonometric polynomials with frequencies only supported by hyperbolic crosses allow for a good approximation of functions of appropriate smoothness and decrease the number of used Fourier coefficients strongly. As a matter of course, an important issue is the customisation of efficient algorithms to these thinner discretisations.

By using rank-1 lattices as spatial discretisations one can simplify the corresponding multidimensional trigonometric polynomials to one dimensionals in an easy way. With the well known FFT one can evaluate these stable and fast. We generalize this concept by using generating vectors with real-valued entries. By doing this, we can give new strategies to search for stable spatial discretisations of trigonometric polynomials.