New cubature formulae and hyperinterpolation
نویسندگان
چکیده
A new algebraic cubature formula of degree 2n + 1 for the product Chebyshev measure in the d-cube with ≈ nd/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 3dimensional FFT. Moreover, integration of the hyperinterpolant provides a new Clenshaw-Curtis type cubature formula in the 3-cube.
منابع مشابه
New Cubature Formulae and Hyperinterpolation in Three Variables
A new algebraic cubature formula of degree 2n+1 for the product Chebyshev measure in the d-cube with ≈ n/2 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 hyperinterpo...
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تاریخ انتشار 2008