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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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THE CUBATURE FORMULAE OF L. A. LYUSTERNIK
Russian Mathematical Surveys, 1970In 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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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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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 Formulas of a Nonalgebraic Degree of Precision
Constructive Approximation, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cools, Ronald, Santos-León, J. C.
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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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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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Fast computation of cubature formulae for the sphere
2017 Hands-free Speech Communications and Microphone Arrays (HSCMA), 2017The near-uniform distribution of nodes on the surface of a sphere has found many uses in numerical integration, physics, chemistry, crystallography, and more recently in the capture, representation and reproduction of spatial audio. A popular solution posed by Fliege and Meyer treats nodes as charged particles that are constrained to lie on the surface
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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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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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On cubature formulas on the basis of lattices
Analysis Mathematica, 1995Construct a sequence of lattice rules for the upper estimation of the value \[ M( P(S_\gamma (n)))= \sup\{|t(\cdot) |_\infty/ |t(\cdot) |_1: t\in P(S_\gamma (n)),\;t\not\equiv 0\} \] for \(n=2\). \(P(S_\gamma (n))\) denotes the class of all nonnegative trigonometric polynomials \(t(x)\) with the spherical spectrum \(S_\gamma(n)\).
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Cubature Formulas of Finite Order
1997We 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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