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. Yang, Sheng-Chun; Qian, Hu-Jun; Lu, Zhong-Yuan: A new theoretical derivation of NFFT and its implementation on GPU (2018)
  2. Adcock, Ben; Gataric, Milana; Hansen, Anders C.: Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples (2017)
  3. Caliari, M.; Ostermann, A.; Piazzola, C.: A splitting approach for the magnetic Schrödinger equation (2017)
  4. Chauffert, Nicolas; Ciuciu, Philippe; Kahn, Jonas; Weiss, Pierre: A projection method on measures sets (2017)
  5. Landa, Boris; Shkolnisky, Yoel: Steerable principal components for space-frequency localized images (2017)
  6. Adcock, Ben; Platte, Rodrigo B.: A mapped polynomial method for high-accuracy approximations on arbitrary grids (2016)
  7. 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)
  8. Boyer, Claire; Chauffert, Nicolas; Ciuciu, Philippe; Kahn, Jonas; Weiss, Pierre: On the generation of sampling schemes for magnetic resonance imaging (2016)
  9. Fornasier, Massimo; Hütter, Jan-Christian: Consistency of probability measure quantization by means of power repulsion-attraction potentials (2016)
  10. Ivanov, Kamen G.; Petrushev, Pencho P.: Highly effective stable evaluation of bandlimited functions on the sphere (2016)
  11. Junghanns, P.; Kaiser, R.; Potts, Daniel: Collocation-quadrature methods and fast summation for Cauchy singular integral equations with fixed singularities (2016)
  12. Marco Caliari, Simone Zuccher: INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections (2016) arXiv
  13. Dong, Yiqiu; Görner, Torsten; Kunis, Stefan: An algorithm for total variation regularized photoacoustic imaging (2015)
  14. Erb, Wolfgang; Mathias, Sonja: An alternative to Slepian functions on the unit sphere -- a space-frequency analysis based on localized spherical polynomials (2015)
  15. Beatson, R.K.; Ong, W.E.; Rychkov, I.: Faster fast evaluation of thin plate splines in two dimensions (2014)
  16. 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)
  17. González, Adriana; Jacques, Laurent; De Vleeschouwer, Christophe; Antoine, Philippe: Compressive optical deflectometric tomography: a constrained total-variation minimization approach (2014)
  18. Kritsikis, E.; Vaysset, A.; Buda-Prejbeanu, L.D.; Alouges, F.; Toussaint, J.-C.: Beyond first-order finite element schemes in micromagnetics (2014)
  19. Lyon, M.; Picard, J.: The Fourier approximation of smooth but non-periodic functions from unevenly spaced data (2014)
  20. Gimbutas, Zydrunas; Veerapaneni, Shravan: A fast algorithm for spherical grid rotations and its application to singular quadrature (2013)

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