Results 1 to 10 of about 113 (109)
Cubature Formulae and Polynomial Ideals
Advances in Applied Mathematics, 1999 The main purpose of this paper is to study the structure of cubature formulae using the notion of a polynomial ideal and its variety. The author proves that if \(I\) is a polynomial ideal generated by a proper set of \((2n-1)\) orthogonal polynomials and if the cardinality of the variety \(V(I)\) is equal to the codimension of \(I\), then there exists ...
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On asymptotically optimal cubatures for multidimensional Sobolev spaces
Researches in Mathematics, 2021 We find an asymptotically optimal method of recovery of the weighted integral for the classes of multivariate functions that are defined via restrictions on their (distributional) gradient.
V.F. Babenko +2 more
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Meshless cubature by Green’s formula [PDF]
Applied Mathematics and Computation, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
SOMMARIVA, ALVISE, VIANELLO, MARCO
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Commuting extensions and cubature formulae [PDF]
Numerische Mathematik, 2005 34 pages, 3 figures ...
Ilan Degani +2 more
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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 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 a class of embedded cubature formulae on the simplex
ACI Avances en Ciencias e Ingenierías, 2014 In this paper we investigate a class of embedded cubature formulae on the simplex announced in [1]. Here we recall the class of formulae, we introduce the remainder and we give an estimation of this, we also investigate the convergence.
Francesco Aldo Costabile, Luca Guzzardi
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The volume integral equation method in magnetostatic problem
Discrete and Continuous Models and Applied Computational Science, 2019 This article addresses the issues of volume integral equation method application to magnetic system calculations. The main advantage of this approach is that in this case finding the solution of equations is reduced to the area filled with ferromagnetic.
Pavel G Akishin, Andrey A Sapozhnikov
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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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