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Cubature Formulae Associated with the Dunkl Laplacian
Results in Mathematics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ben Salem, Néjib, Touahri, Kamel
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Cubature Formulae for Polyharmonic Functions
2001We construct cubature formulae for the ball in ℝd, based on integrals of the function v(x), its normal derivatives or iterated Laplacians △ j v (j = 0,…, m i−1) over n distinct (d−1)dimensional hyperspheres S(ρ i )of radius ρ i , respectively, which integrate exactly wide classes of functions defined as the harmonic span of given radial functions, and ...
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Fast computation of cubature formulae for the sphere
Joint Workshop on Hands-free Speech Communication and Microphone Arrays, 2017Mark R. P. Thomas
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Invariant Laplacian-involving cubature formulas
Computational Mathematics and Mathematical Physics, 2015For integrals in n dimensions over a hypercube, two ninth-degree cubature formulas that are invariant with respect to a hyperoctahedral group are constructed. The cubature sums of these formulas contain the Laplacian. Examples are given in which approximate values of the formulas’ parameters are presented in the form of tables.
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Schmid's approach on cubature formulae
International Journal of Computer Mathematics, 1990Schmid's method [1] is applied to establish a fourth and a sixth degree formulae with respect to the weight function x 1/2 where the region of integration is the set Ω defined by Ω = {(x,y): x∊[0,l] and y∊ [−1,1]}
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Cubature formulae and orthogonal polynomials
USSR Computational Mathematics and Mathematical Physics, 1969Abstract IN [1] the proposition (Theorem 2' ) was stated that k1 common zeros of two orthogonal polynomials of degree k of a plane domain and with a positive weight function, can be taken as the nodes of a cubature formula exact for polynomials of degree 2 k — 1.
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Weighted spherical semidesigns and cubature formulae for calculating integrals on a sphere
Russian Mathematics (Izvestiya VUZ. Matematika), 2013N. O. Kotelina, A. B. Pevnyi
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THE CUBATURE FORMULAE OF L. A. LYUSTERNIK
Russian Mathematical Surveys, 1970In this paper a short survey is given of the work of L.A. Lyusternik on cubature formulae, which are many-dimensional generalizations of the standard quadrature formulae of Gauss for an interval. A general method is developed for constructing such formulae; a number of specific formulae are given and certain applications are made to the solution of ...
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Model analysis and optimization under uncertainty using thinned cubature formulae
Computers and Chemical Engineering, 2016F. Bernardo
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