Bivariate Lagrange interpolation at the Padua points: Computational aspects

Authors:
Marco Caliari;Stefano De Marchi;Marco Vianello
Affiliations:
Department of Pure and Applied Mathematics, University of Padua, via Trieste 63, 35121 Padova, Italy;Department of Computer Science, University of Verona S.da Le Grazie 15, 37134 Verona, Italy;Department of Pure and Applied Mathematics, University of Padua, via Trieste 63, 35121 Padova, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

The so-called ''Padua points'' give a simple, geometric and explicit construction of bivariate polynomial interpolation in the square. Moreover, the associated Lebesgue constant has minimal order of growth O(log^2(n)). Here we show four families of Padua points for interpolation at any even or odd degree n, and we present a stable and efficient implementation of the corresponding Lagrange interpolation formula, based on the representation in a suitable orthogonal basis. We also discuss extension of (non-polynomial) Padua-like interpolation to other domains, such as triangles and ellipses; we give complexity and error estimates, and several numerical tests.