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. Barnett, Alex H.: How exponentially ill-conditioned are contiguous submatrices of the Fourier matrix? (2022)
  2. Bartel, Felix; Hielscher, Ralf: Concentration inequalities for cross-validation in scattered data approximation (2022)
  3. Diao, Xuhao; Hu, Jun; Ma, Suna: Preconditioned Legendre spectral Galerkin methods for the non-separable elliptic equation (2022)
  4. Jafarzadeh, Siavash; Mousavi, Farzaneh; Larios, Adam; Bobaru, Florin: A general and fast convolution-based method for peridynamics: applications to elasticity and brittle fracture (2022)
  5. Medvedev, Sergey; Chekhovskoy, Igor; Vaseva, Irina; Fedoruk, Mikhail: Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system associated with nonlinear Schrödinger equation (2022)
  6. Mildenberger, Sophie; Quellmalz, Michael: Approximation properties of the double Fourier sphere method (2022)
  7. Potts, D.; Schmischke, M.: Learning multivariate functions with low-dimensional structures using polynomial bases (2022)
  8. Barnett, Alex H.: Aliasing error of the (\exp(\beta\sqrt1-z^2)) kernel in the nonuniform fast Fourier transform (2021)
  9. Bergermann, Kai; Stoll, Martin; Volkmer, Toni: Semi-supervised learning for aggregated multilayer graphs using diffuse interface methods and fast matrix-vector products (2021)
  10. Gimeno, Joan; Yang, Jiaqi; de la Llave, Rafael: Numerical computation of periodic orbits and isochrons for state-dependent delay perturbation of an ODE in the plane (2021)
  11. Goncharov, Fedor: A geometric based preprocessing for weighted ray transforms with applications in SPECT (2021)
  12. Kirisits, Clemens; Quellmalz, Michael; Ritsch-Marte, Monika; Scherzer, Otmar; Setterqvist, Eric; Steidl, Gabriele: Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations (2021)
  13. Koga, Kazuki: Signal processing approach to mesh refinement in simulations of axisymmetric droplet dynamics (2021)
  14. Potts, Daniel; Tasche, Manfred: Continuous window functions for NFFT (2021)
  15. Potts, Daniel; Tasche, Manfred: Uniform error estimates for nonequispaced fast Fourier transforms (2021)
  16. Averseng, Martin: Fast discrete convolution in (\mathbbR^2) with radial kernels using non-uniform fast Fourier transform with nonequispaced frequencies (2020)
  17. Bartel, Felix; Hielscher, Ralf; Potts, Daniel: Fast cross-validation in harmonic approximation (2020)
  18. Lazarus, Carole; März, Maximilian; Weiss, Pierre: Correcting the side effects of ADC filtering in MR image reconstruction (2020)
  19. Rangan, Aaditya; Spivak, Marina; Andén, Joakim; Barnett, Alex: Factorization of the translation kernel for fast rigid image alignment (2020)
  20. Wülker, Christian: Fast SGL Fourier transforms for scattered data (2020)

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