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Polynomial approximation and quadrature on geographic rectangles

Author

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  • Gentile, M.
  • Sommariva, A.
  • Vianello, M.

Abstract

Using some recent results on subperiodic trigonometric interpolation and quadrature, and the theory of admissible meshes for multivariate polynomial approximation, we study product Gaussian quadrature, hyperinterpolation and interpolation on some regions of Sd,d ≥ 2. Such regions include caps, zones, slices and more generally spherical rectangles defined on S2 by longitude and (co)latitude (geographic rectangles). We provide the corresponding Matlab codes and discuss several numerical examples on S2.

Suggested Citation

  • Gentile, M. & Sommariva, A. & Vianello, M., 2017. "Polynomial approximation and quadrature on geographic rectangles," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 159-179.
    • Handle: RePEc:eee:apmaco:v:297:y:2017:i:c:p:159-179
    DOI: 10.1016/j.amc.2016.08.014
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    References listed on IDEAS

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    1. Sommariva, Alvise & Vianello, Marco, 2015. "Polynomial fitting and interpolation on circular sections," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 410-424.
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