Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms NFFT 3 is a software library that implements the nonequispaced fast Fourier transform (NFFT) and a number of related algorithms, for example, nonequispaced fast Fourier transforms on the sphere and iterative schemes for inversion. This article provides a survey on the mathematical concepts behind the NFFT and its variants, as well as a general guideline for using the library. Numerical examples for a number of applications are given.

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  1. Adcock, Ben; Platte, Rodrigo B.: A mapped polynomial method for high-accuracy approximations on arbitrary grids (2016)
  2. Andersson, Fredrik; Carlsson, Marcus; Nikitin, Viktor V.: Fast algorithms and efficient GPU implementations for the Radon transform and the back-projection operator represented as convolution operators (2016)
  3. Fornasier, Massimo; Hütter, Jan-Christian: Consistency of probability measure quantization by means of power repulsion-attraction potentials (2016)
  4. Ivanov, Kamen G.; Petrushev, Pencho P.: Highly effective stable evaluation of bandlimited functions on the sphere (2016)
  5. Junghanns, P.; Kaiser, R.; Potts, Daniel: Collocation-quadrature methods and fast summation for Cauchy singular integral equations with fixed singularities (2016)
  6. Dong, Yiqiu; Görner, Torsten; Kunis, Stefan: An algorithm for total variation regularized photoacoustic imaging (2015)
  7. Erb, Wolfgang; Mathias, Sonja: An alternative to Slepian functions on the unit sphere -- a space-frequency analysis based on localized spherical polynomials (2015)
  8. Beatson, R.K.; Ong, W.E.; Rychkov, I.: Faster fast evaluation of thin plate splines in two dimensions (2014)
  9. Dahlke, Stephan (ed.); Dahmen, Wolfgang (ed.); Griebel, Michael (ed.); Hackbusch, Wolfgang (ed.); Ritter, Klaus (ed.); Schneider, Reinhold (ed.); Schwab, Christoph (ed.); Yserentant, Harry (ed.): Extraction of quantifiable information from complex systems (2014)
  10. Kritsikis, E.; Vaysset, A.; Buda-Prejbeanu, L.D.; Alouges, F.; Toussaint, J.-C.: Beyond first-order finite element schemes in micromagnetics (2014)
  11. Lyon, M.; Picard, J.: The Fourier approximation of smooth but non-periodic functions from unevenly spaced data (2014)
  12. Gimbutas, Zydrunas; Veerapaneni, Shravan: A fast algorithm for spherical grid rotations and its application to singular quadrature (2013)
  13. Martin, F.; Wegert, E.: Computing the Hilbert transform using biorthogonal spline wavelets (2013)
  14. Pippig, Michael; Potts, Daniel: Parallel three-dimensional nonequispaced fast Fourier transforms and their application to particle simulation (2013)
  15. Görner, Torsten; Hielscher, Ralf; Kunis, Stefan: Efficient and accurate computation of spherical mean values at scattered center points (2012)
  16. Gräf, Manuel; Potts, Daniel; Steidl, Gabriele: Quadrature errors, discrepancies, and their relations to halftoning on the torus and the sphere (2012)
  17. Kämmerer, Lutz; Kunis, Stefan; Potts, Daniel: Interpolation lattices for hyperbolic cross trigonometric polynomials (2012)
  18. Kunis, Stefan; Melzer, Ines: A stable and accurate butterfly sparse Fourier transform (2012)
  19. Gräf, Manuel; Potts, Daniel: On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms (2011)
  20. Peter, Thomas; Potts, Daniel; Tasche, Manfred: Nonlinear approximation by sums of exponentials and translates (2011)

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