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Polynomial Interpolation on the Unit Sphere and on the Unit Ball

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Abstract

The problem of interpolation on the unit sphere S d by spherical polynomials of degree at most n is shown to be related to the interpolation on the unit ball B d by polynomials of degree n. As a consequence several explicit sets of points on S d are given for which the interpolation by spherical polynomials has a unique solution. We also discuss interpolation on the unit disc of R 2 for which points are located on the circles and each circle has an even number of points. The problem is shown to be related to interpolation on the triangle in a natural way.

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR, 97403-1222, USA

    Yuan Xu

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  1. Yuan Xu
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Xu, Y. Polynomial Interpolation on the Unit Sphere and on the Unit Ball. Advances in Computational Mathematics 20, 247–260 (2004). https://doi.org/10.1023/A:1025851005416

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  • DOI: https://doi.org/10.1023/A:1025851005416

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