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 (log2 (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.

Bivariate Lagrange interpolation at the Padua points: Computational aspects

CALIARI, Marco;DE MARCHI, Stefano;
2008-01-01

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 (log2 (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.
bivariate interpolation; Padua points; linear algebra
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/339197
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