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Numerical hyperinterpolation over nonstandard planar regions

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  • Sommariva, Alvise
  • Vianello, Marco

Abstract

We discuss an algorithm (implemented in Matlab) that computes numerically total-degree bivariate orthogonal polynomials (OPs) given an algebraic cubature formula with positive weights, and constructs the orthogonal projection (hyperinterpolation) of a function sampled at the cubature nodes. The method is applicable to nonstandard regions where OPs are not known analytically, for example convex and concave polygons, or circular sections such as sectors, lenses and lunes.

Suggested Citation

  • Sommariva, Alvise & Vianello, Marco, 2017. "Numerical hyperinterpolation over nonstandard planar regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 110-120.
    • Handle: RePEc:eee:matcom:v:141:y:2017:i:c:p:110-120
    DOI: 10.1016/j.matcom.2016.07.009
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    Cited by:

    1. Sommariva, A. & Vianello, M., 2021. "Numerical hyperinterpolation over spherical triangles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 15-22.

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