Abstract
A new algebraic cubature formula of degree 2n+1 for the product Chebyshev measure in the d-cube with ≈n d/2d−1 nodes is established. The new formula is then applied to polynomial hyperinterpolation of degree n in three variables, in which coefficients of the product Chebyshev orthonormal basis are computed by a fast algorithm based on the 3-dimensional FFT. Moreover, integration of the hyperinterpolant provides a new Clenshaw-Curtis type cubature formula in the 3-cube.
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Communicated by T. Lyche.
Work supported by the National Science Foundation under Grant DMS-0604056, by the “ex-60%” funds of the Universities of Padova and Verona, and by the INdAM-GNCS.
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De Marchi, S., Vianello, M. & Xu, Y. New cubature formulae and hyperinterpolation in three variables. Bit Numer Math 49, 55–73 (2009). https://doi.org/10.1007/s10543-009-0210-7
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DOI: https://doi.org/10.1007/s10543-009-0210-7