Fast interpolation and quadrature at the Padua points ∗
Stefano De Marchi Department of Computer Science
University of Verona
S.da Le Grazie 15, 37134 - Verona (Italy)
Abstract
The Padua points are the first known example of optimal points for total degree polynomial interpolation in two variables, with a Lebesgue constant increasing like log
2of the degree. Moreover, similarly to the one-dimensional case, they generate a (nontensorial) Clenshaw-Curtis-like quadrature formula that turns out to be competitive with the tensorial Gauss-Legendre formula and even with the few known minimal formulas in the square, on integrands that are not “too regular”. We present new fast algorithms for interpolation and numerical quadrature at the Padua points, and some applications.
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