IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Fast Memory Efficient Evaluation of Spherical Polynomials at Scattered Points


A 2013 Preprint by K. Ivanov and P. Petrushev

  • 2013:05
  • A method for fast evaluation of band-limited functions (spherical polynomials) at many scattered points on the unit 2-d sphere is presented. The method relies on the superb localization of the father needlet kernels and their compatibility with spherical harmonics. It is fast, local, memory efficient, numerically stable and with guaranteed (prescribed) accuracy. The speed is independent of the band limit and depends logarithmically on the prescribed accuracy. The method can be also applied for approximation on the sphere, verifi cation of spherical polynomials and for fast generation of surfaces in computer-aided geometric design. It naturally extends to higher dimensions.

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