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On Trigonometric Blending Interpolation and Cubature Formulae
Results in Mathematics, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dryanov, Dimiter, Petrov, Petar
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Cubature Formulae, Polytopes, and Spherical Designs
1981The 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 Formulae of Even Degree
Common zeros of polynomials in several variables and higher dimensional quadrature, 2020Yuan Xu
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Multidimensional Cubature Formulas with Superpower Convergence
Doklady Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Belov A.A., Tintul M.A.
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Asymmetric Cubature Formulae with Few Points in High Dimension for Symmetric Measures
SIAM Journal on Numerical Analysis, 2004Nicolas Victoir
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Compound cubature formulas on a lattice
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023In 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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The algebra of interpolatory cubature formulæ for generic nodes
Statistics and computing, 2013We consider the classical problem of computing the expected value of a real function f of the d-variate random variable X using cubature formulæ. We use in synergy tools from Commutative Algebra for cubature rulæ, from elementary orthogonal polynomial ...
C. Fassino +2 more
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Multivariate Gaussian cubature formulae
Archiv der Mathematik, 1995Gaussian quadrature can be briefly described as follows: There is a one- parameter family of minimal formulae of degree \(2n-2\) the nodes of which are the roots of \(p_ n+ \rho p_{n-1}\), \(\rho\neq 0\), where \(\{p_ n\}_{n=0}^ \infty\), denotes the system of orthogonal polynomials w.r.t.
Berens, H., Schmid, H. J., Xu, Y.
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Bivariate Cardinal Interpolation and Cubature Formulas
SIAM Journal on Numerical Analysis, 1975We 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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ARCANE: Scalable high-degree cubature formulae for simulating SDEs without Monte Carlo error
arXiv.orgMonte Carlo sampling is the standard approach for estimating properties of solutions to stochastic differential equations (SDEs), but accurate estimates require huge sample sizes. Lyons and Victoir (2004) proposed replacing independently sampled Brownian
Peter Koepernik, Thomas Coxon, J. Foster
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