Results 111 to 120 of about 1,445 (171)

The cubature formulas computing modeling

Informatization and communication, 2021
Presented paper is related with the problem of hybrid computing structures design and their methodology. The main purpose is the theoretical basis for the automated design supercomputing devices development and the different restrictions accounting.
N.S. Krivsha, S.A. Butenkov, V.V. Krivsha   +2 more
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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, Polytopes, and Spherical Designs

1981
The construction of a cubature formula of strength t for the unit sphere Ω d in ℝ d amounts to finding finite sets X 1,..., X N ⊂ Ω d and coefficients a 1,..., a N ∈ ℝ such that|Ωd|−1∫Ωdf(ξ)dω(ξ)=∑i=1Nai|Xi|−1∑x∈Xιf(x),(1.1)for all functions f represented on Ω d by polynomials of degree ⩽ t; cf. [16], [15], [11]. Sobolev [14,15] introduced group theory
Goethals, J.M., Seidel, J.J.
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Cubature Formulas of Finite Order

1997
We speak about a cubature formula of infinite order whenever the error of the formula is O(h m ) for all integer m and all functions in the space under study. Here h is the mesh-size of the lattice of integration. The Mean Value Theorem for harmonic functions provides the simplest example of a formula of such kind. In § 6 and § 8 of the current section
S. L. Sobolev, V. L. Vaskevich
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Theory of Cubature Formulas

2006
The problems of the theory of cubature formulas, when we study their error functionals in the corresponding functional spaces, can be treated as problems of functional analysis. In particular, applying certain Hilbert metrics and solving the appearing problems by the methods of variations calculus, we can obtain exact estimates of the norms of error ...
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Cubature formulae for Besov classes

Izvestiya: Mathematics, 1997
Summary: This paper is devoted to an investigation of optimal cubature formulae for Besov classes of functions with restrictions on the mixed difference. This study is a continuation of papers [Mat. Zametki 49, No. 1, 149-151 (1991; Zbl 0760.41017)] and Mat. Sb. 183, No. 7, 23-34 (1992; Zbl 0786.41025)].
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Simple Cubature Formulas with High Polynomial Exactness

Constructive Approximation, 1999
The authors study cubature formulas for \(d\)-dimensional integrals with arbitrary weight function of tensor product form. They construct formulas that yield a high polynomial exactness. If the degree of accuracy is fixed then the number of knots depends on the dimension in an order-optimal way.
Novak, Erich, Ritter, Klaus
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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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Cubature Formulas with Regular Boundary Layer

2006
In this chapter we show that cubature formulas with regular boundary layer are asymptoticallymath-optimal as the lattice mesh-size vanishes.
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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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