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CUBATURE FORMULAS ON TRIANGLE
"... Abstract. In this article are presented some cubature formulas on triangle T which are obtained by the product of known quadrature formulas and some formulas obtaining by an approximation formula on triangle. 1. ..."
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Abstract. In this article are presented some cubature formulas on triangle T which are obtained by the product of known quadrature formulas and some formulas obtaining by an approximation formula on triangle. 1.
CALCULATING THE GREEKS BY CUBATURE FORMULAS
, 2004
"... We provide cubature formulas for the calculation of derivatives of expected values in the spririt of Terry Lyons and Nicolas Victoir. In financial mathematics derivatives of option prices with respect to initial values, so called Greeks, are of particular importance as hedging parameters. Cubature ..."
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Cited by 4 (1 self)
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We provide cubature formulas for the calculation of derivatives of expected values in the spririt of Terry Lyons and Nicolas Victoir. In financial mathematics derivatives of option prices with respect to initial values, so called Greeks, are of particular importance as hedging parameters. Cubature
Cubature Formulae and Orthogonal Polynomials
, 2000
"... The connection between orthogonal polynomials and cubature formulae for the approximation of multivariate integrals has been studied for about 100 years. The article J. Radon published about 50 years ago has been very inuential. In this text we describe some of the results that were obtained during ..."
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Cited by 11 (0 self)
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The connection between orthogonal polynomials and cubature formulae for the approximation of multivariate integrals has been studied for about 100 years. The article J. Radon published about 50 years ago has been very inuential. In this text we describe some of the results that were obtained during
Commuting extensions and cubature formulae
"... Abstract Based on a novel point of view on 1dimensional Gaussian quadrature, we present a new approach to ddimensional cubature formulae. It is well known that the nodes of 1dimensional Gaussian quadrature can be computed as eigenvalues of the socalled Jacobi matrix. The ddimensional analog is ..."
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Cited by 3 (0 self)
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Abstract Based on a novel point of view on 1dimensional Gaussian quadrature, we present a new approach to ddimensional cubature formulae. It is well known that the nodes of 1dimensional Gaussian quadrature can be computed as eigenvalues of the socalled Jacobi matrix. The ddimensional analog
CUBATURE FORMULAS, GEOMETRICAL DESIGNS,
"... Abstract. Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way, several known results for spheres in Euclidean spaces ..."
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Abstract. Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way, several known results for spheres in Euclidean
Cubature Formulas in Higher Dimensions
, 2008
"... We study cubature formulas for ddimensional integrals with an arbitrary symmetric weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixed degree ℓ = 5 or ℓ = 7 and large dimension d the number of knots is only slightly larger than the low ..."
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We study cubature formulas for ddimensional integrals with an arbitrary symmetric weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixed degree ℓ = 5 or ℓ = 7 and large dimension d the number of knots is only slightly larger than
Norming Sets and Spherical Cubature Formulas
, 1998
"... We investigate the construction of cubature formulas for the unit sphere in R^n that have almost equal weights. The corresponding knots are taken from equidistributed point sets on the sphere. The notion of norming sets in connection with the Markov inequality of spherical harmonics is used in ord ..."
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Cited by 13 (3 self)
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We investigate the construction of cubature formulas for the unit sphere in R^n that have almost equal weights. The corresponding knots are taken from equidistributed point sets on the sphere. The notion of norming sets in connection with the Markov inequality of spherical harmonics is used
Minimal cubature formulae of trigonometric degree
 Math. Comp
, 1996
"... Abstract. 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. 1. ..."
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Cited by 10 (3 self)
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Abstract. 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. 1.
Cubature formula and interpolation on the cubic domain
 NUMER. MATH.: THEORY METHOD APPL., ACCEPTED FOR PUBLICATION
, 2008
"... Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation pol ..."
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Cited by 3 (3 self)
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Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation
Results 1  10
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1,077