Near-optimal interpolation and quadrature in two variables: the Padua points∗
نویسنده
چکیده
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 of the degree; cf. [1, 2, 3]. Moreover, they generate a nontensorial Clenshaw-Curtis-like cubature formula, which 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”; cf. [4]. Such a behavior is analogous to that of the univariate Clenshaw-Curtis formula; cf. [5]. We present a survey about properties, software implementations and applications of interpolation and numerical cubature at the Padua points.
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