High-Dimensional FFT

  • Gerlind Plonka
  • Daniel Potts
  • Gabriele Steidl
  • Manfred Tasche
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


In this chapter, we discuss methods for the approximation of d-variate functions in high dimension \(d\in \mathbb N\) based on sampling along rank-1 lattices and we derive the corresponding fast algorithms. In contrast to Chap.  4, our approach to compute the Fourier coefficients of d-variate functions is no longer based on tensor product methods.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Gerlind Plonka
    • 1
  • Daniel Potts
    • 2
  • Gabriele Steidl
    • 3
  • Manfred Tasche
    • 4
  1. 1.University of GöttingenGöttingenGermany
  2. 2.Chemnitz University of TechnologyChemnitzGermany
  3. 3.TU KaiserslauternKaiserslauternGermany
  4. 4.University of RostockRostockGermany

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