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Equidistribution of Fekete Points on the Sphere

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Abstract

Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well-suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points on the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz–Zygmund arrays and interpolating arrays, that have been studied recently.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Jordi Marzo

  2. Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Joaquim Ortega-Cerdà

Authors
  1. Jordi Marzo
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  2. Joaquim Ortega-Cerdà
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Corresponding author

Correspondence to Jordi Marzo.

Additional information

Communicated by Edward B. Saff.

Supported by projects MTM2008-05561-C02-01, 2005SGR00611 and (the first author) NordForsk Research Network “Analysis and Applications” grant # 080151.

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Marzo, J., Ortega-Cerdà, J. Equidistribution of Fekete Points on the Sphere. Constr Approx 32, 513–521 (2010). https://doi.org/10.1007/s00365-009-9051-5

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  • DOI: https://doi.org/10.1007/s00365-009-9051-5

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