Cubature Formulae and Polynomial Ideals
نویسندگان
چکیده
منابع مشابه
New cubature formulae and hyperinterpolation
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 hyperin...
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Based on a novel point of view on 1-dimensional Gaussian quadrature, we present a new approach to d-dimensional cubature formulae. It is well known that the nodes of 1-dimensional Gaussian quadrature can be computed as eigenvalues of the so-called Jacobi matrix. The d-dimensional analog is that cubature nodes can be obtained from the eigenvalues of certain mutually commuting matrices. These are...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1999
ISSN: 0196-8858
DOI: 10.1006/aama.1999.0652