An encyclopaedia of cubature formulas

Authors:
Ronald Cools
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium
Venue:
Journal of Complexity
Year:
2003

Citing 5
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An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations

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Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements

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Numerical studies of time-independent and time-dependent scattering by several elliptical cylinders

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Hyperinterpolation in the cube

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Performance of numerically computed quadrature points

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Asymmetric cubature formulas for polynomial integration in the triangle and square

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Numerical integration formulas of degree two

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Uncertainty quantification using polynomial chaos expansion with points of monomial cubature rules

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Computing approximate Fekete points by QR factorizations of Vandermonde matrices

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Newton-Cotes cubature rules over (d+1)-pencil lattices

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A fourth degree integration formula for the n-dimensional simplex

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Product Gauss quadrature rules vs. cubature rules in the meshless local Petrov-Galerkin method

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Improved cubature formulae of high degrees of exactness for the square

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An adaptive numerical integration algorithm for polygons

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Probability density evolution analysis of engineering structures via cubature points

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Constructing cubature formulae of degree 5 with few points

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High-degree cubature Kalman filter

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Bayesian analysis of GUHA hypotheses

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Abstract

About 13 years ago we started collecting published cubature formulas for the approximation of multivariate integrals over some standard regions. In this paper we describe how we make this information available to a larger audience via the World Wide Web.