On generalized invariant cubature formulae
نویسندگان
چکیده
منابع مشابه
Invariant Cubature Formulae for Spheres and Balls
Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282–290] for the unit weight function on T d. These formulae are used to derive cubature formulae on the surface of the sphere Sd and on the unit ball Bd using connections between cubature for...
متن کاملInvariant Cubature Formulae for Spheres and Balls by Combinatorial Methods
Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282–290] for the unit weight function on T . These formulae are used to derive cubature formulae on the surface of the sphere S and on the unit ball B using connections between cubature formul...
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The construction of (near-)minimal cubature formulae on the disk is still a complicated subject on which many results have been published.We restrict ourselves to the case of radial weight functions and make use of a recent connection between cubature and the concept of multivariate spherical orthogonal polynomials to derive a new system of equations defining the nodes and weights of (near-)min...
متن کاملNew 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...
متن کاملCommuting extensions and cubature formulae
Based on a novel point of view on 1-dimensional Gaussian quadrature, we present a new approach to the computation of 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 ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(99)00377-5