Results 111 to 120 of about 173 (155)

Invariant cubature formulas for the hyperoctahedron

Mathematical Notes, 1997
Cubature formulas for integrals over the hyperoctahedron \(O_{n}\) in \({\mathbb{R}}^{n}\) are derived. These formulas are invariant under the group of all orthogonal transformations of \(O_{n}\). The result is based on a theorem by S. L. Sobolev (1962).
exaly   +3 more sources

Compound cubature formulas on a lattice

Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023
In the present paper lattice optimal cubature formulas are constructed by the variational method in the Sobolev space. In addition, the square of the norm of the error functional of the constructed lattice optimal cubature formulas in the conjugate Sobolev space is explicitly calculated.
Shadimetov, Kh. M., Mamatova, N. Kh.
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Multidimensional Cubature Formulas with Superpower Convergence

Doklady Mathematics, 2023
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Belov A.A., Tintul M.A.
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The construction of cubature formulae by continuation

Computing, 1990
A cubature formula Q is an approximation of an n-dimensional integral I. Q is exact for the space spanned by the polynomials \(f_ 1,...,f_ d\) if it verifies the system of equations: \(Q[f_ i]=I[f_ i]\quad i=1,...,d.\) The unknowns are knots and weights of the cubature formula. We suppose that there are as many unknowns as equations.
Pierre Verlinden, Ann Haegemans
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Bivariate Cardinal Interpolation and Cubature Formulas

SIAM Journal on Numerical Analysis, 1975
We introduce a bivariate cardinal interpolation series for a function $f(x,u)$ analogous to the Whittaker’s cardinal function. Under suitable conditions on f, we establish the convergence of the bivariate cardinal series; and under additional conditions, the convergence of the cardinal series to f.
Chawla, M. M., Jayarajan, N.
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Cubature Formulas on Spheres

2013
In problems that deal with data, as frequently encountered in applied mathematics, it is often necessary to discretize integrals to obtain discrete processes of approximation. Cubature formulas, a synonym for numerical integration formulas, are essential tools for discretizing integrals.
Feng Dai, Yuan Xu
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Cubature Formulae Associated with the Dunkl Laplacian

Results in Mathematics, 2010
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Ben Salem, Néjib, Touahri, Kamel
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On Trigonometric Blending Interpolation and Cubature Formulae

Results in Mathematics, 2012
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Dryanov, Dimiter, Petrov, Petar
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THE CUBATURE FORMULAE OF L. A. LYUSTERNIK

Russian Mathematical Surveys, 1970
In 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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Cubature Formulas of a Nonalgebraic Degree of Precision

Constructive Approximation, 2002
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Cools, Ronald, Santos-León, J. C.
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