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Computational Methods for the Fourier Analysis of Sparse High-Dimensional Functions

  • Lutz Kämmerer
  • Stefan Kunis
  • Ines Melzer
  • Daniel Potts
  • Toni Volkmer
Chapter
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 102)

Abstract

A straightforward discretisation of high-dimensional problems often leads to a curse of dimensions and thus the use of sparsity has become a popular tool. Efficient algorithms like the fast Fourier transform (FFT) have to be customised to these thinner discretisations and we focus on two major topics regarding the Fourier analysis of high-dimensional functions: We present stable and effective algorithms for the fast evaluation and reconstruction of multivariate trigonometric polynomials with frequencies supported on an index set \(\mathcal{I}\subset \mathbb{Z}^{d}\).

Keywords

Fast Fourier Transform Fourier Coefficient Trigonometric Polynomial Sparse Grid Matrix Vector Multiplication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We gratefully acknowledge support by the German Research Foundation (DFG) within the Priority Program 1324, project PO 711/10-2 and KU 2557/1-2. Moreover, Ines Melzer and Stefan Kunis gratefully acknowledge their support by the Helmholtz Association within the young investigator group VH-NG-526.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lutz Kämmerer
    • 1
  • Stefan Kunis
    • 2
  • Ines Melzer
    • 2
  • Daniel Potts
    • 1
  • Toni Volkmer
    • 1
  1. 1.Technical University of ChemnitzChemnitzGermany
  2. 2.University of OsnabrückOsnabrückGermany

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