Results 11 to 20 of about 173 (155)
On bivariate Gaussian cubature formulae [PDF]
Proceedings of the American Mathematical Society, 1994 It is shown that for two classes of integrals the results of Gaussian quadrature can be extended straightforwardly to the bivariate case. For these classes Gaussian formulae of an arbitrary degree are derived.
Schmid, H. J., Xu, Yuan
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On an Optimal Quadrature Formula for Classes of Functions Given by Modulus of Continuity
Моделирование и анализ информационных систем, 2014 The problem of minimizing the error of a cubature formula on the classes of functions given by modulus of continuity for cubature formulas with fixed nodes on the boundary of gird rectangular localization domain of nodes is considered.
M. Sh. Shabozov
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On a Family of Cubature Formulae [PDF]
The Computer Journal, 1966 Here, 2n + 1 is the degree of precision of the cubature formula, that is, the truncation error indicated by O(h + ) in (2) is zero when F is a polynomial in X and Y with a joint degree smaller than or at most equal to 2/i + l. The N* points Ph at which the function values are sampled, will be called sample points.
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ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS
Acta Polytechnica, 2016 The aim of this article is to describe several cubature formulas related to the Weyl group orbit functions, i.e. to the special cases of the Jacobi polynomials associated to root systems.
Lenka Háková +2 more
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Optimal cubature formulas for approximate integrals of functions defined on a sphere in three-dimensional space [PDF]
E3S Web of ConferencesThe development of effective methods of approximate calculation of integrals using optimal cubature formulas and optimal quadrature formulas with trigonometric weights for defined functions on a sphere, the creation of new algorithms for approximate ...
Bozarov Bakhromjon +5 more
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The Approximate Integrals by the Reproducing Kernel Method on the Elliptical Region Eₙ In the Space Rⁿ [PDF]
مجلة جامعة النجاح للأبحاث العلوم الطبيعيةIn this paper, we applied the reproducing kernel method on elliptical region, we establish the formulas of the reproducing kernel from several degrees and generalized those formulas whatever the dimension of space, we obtained all surfaces, points, and ...
Hiba Aslan, Hamed Abbas
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On some cubature formulas on the sphere
Journal of Approximation Theory, 2006 AbstractWe construct interpolatory cubature rules on the two-dimensional sphere, using the fundamental system of points obtained by Laín Fernández [Polynomial Bases on the Sphere, Logos-Verlag, Berlin, 2003; Localized polynomial bases on the sphere, Electron. Trans. Numer. Anal. 19 (2005) 84–93].
Jürgen Prestin, Daniela Rosca
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Minimal cubature formulae of trigonometric degree [PDF]
Mathematics of Computation, 1996 In this paper we construct minimal cubature formulae of trigonometric degree: we obtain explicit formulae for low dimensions of arbitrary degree and for low degrees in all dimensions. A useful tool is a closed form expression for the reproducing kernels in two dimensions.
Ronald Cools, Ian H. Sloan
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Osculatory and Hyperosculatory Cubature Formulas [PDF]
Mathematics of Computation, 1977 Osculatory and hyperosculatory cubature formulas for a rectangular region, employing the function with either first, or first and second partial derivatives, were obtained together with dominant remainder terms involving higher derivatives at one point, providing exact accuracy through the fifth (seventh) degree without (with) remainders.
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International Journal of Mathematics and Mathematical Sciences, 1983 A numerical technique, first reported in 1979 in refs.[1] and [2], for the numerical evaluation of two-dimensional Cauchy-type principal-value integrals, is extended in this paper to include several cubature formlas of the Radau and Lobatto types.
P. S. Theocaris
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