Abstract
We extend Clenshaw–Curtis quadrature to the square in a nontensorial way, by using Sloan’s hyperinterpolation theory and two families of points recently studied in the framework of bivariate (hyper)interpolation, namely the Morrow–Patterson–Xu points and the Padua points. The construction is an application of a general approach to product-type cubature, where we prove also a relevant stability theorem. The resulting cubature formulas turn out to be competitive on nonentire integrands with tensor-product Clenshaw–Curtis and Gauss–Legendre formulas, and even with the few known minimal formulas.
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Work supported by the “ex-60%” funds of the University of Padova, and by the INdAM GNCS.
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Sommariva, A., Vianello, M. & Zanovello, R. Nontensorial Clenshaw–Curtis cubature. Numer Algor 49, 409–427 (2008). https://doi.org/10.1007/s11075-008-9203-x
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DOI: https://doi.org/10.1007/s11075-008-9203-x
Keywords
- Orthogonal polynomials
- Hyperinterpolation
- Quadrature
- Cubature
- Orthogonal moments
- Nontensorial bivariate Clenshaw–Curtis formulas
- Morrow–Patterson–Xu points
- Padua points