New cubature formulae and hyperinterpolation in three variables

Details New cubature formulae and hyperinterpolation in three variables New cubature formulae and hyperinterpolation in three variables

2008-05-22

arxiv.org/abs/0805.3529v1

Mathematics

Numerical Analysis

Scientific paper

A new algebraic cubature formula of degree $2n+1$ for the product Chebyshev measure in the $d$-cube with $\approx n^d/2^{d-1}$ 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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