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An encyclopaedia of cubature formulas. (English) Zbl 1061.41020
Summary: 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.

MSC:
41A55 Approximate quadratures
65D30 Numerical integration
65D32 Numerical quadrature and cubature formulas
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References:
[1] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, Vol. 55, US Government Printing Office, Washington, DC, 1964. · Zbl 0171.38503
[2] Bailey, D.H., A Fortran-90 based multiprecision system, ACM trans. math. software, 21, 4, 379-387, (1995) · Zbl 0883.68017
[3] R. Cools, Constructing cubature formulae: The science behind the art, Acta Numerica, Vol. 6, Cambridge University Press, Cambridge, 1997, pp. 1-54. · Zbl 0887.65028
[4] Cools, R., Monomial cubature rules Since “stroud”a compilation—part 2, J. comput. appl. math., 112, 1-2, 21-27, (1999) · Zbl 0954.65021
[5] Cools, R.; Rabinowitz, P., Monomial cubature rules Since “stroud”a compilation, J. comput. appl. math., 48, 309-326, (1993) · Zbl 0799.65027
[6] D.W. Lozier, B.R. Miller, B.V. Saunders, Design of a digital mathematical library for science, technology and education, in: Proceedings of the IEEE Forum on Research and Technology Advances in Digital Libraries; IEEE ADL ’99, Baltimore, MD, May 19, 1999.
[7] J. More, B. Garbow, K. Hillstrom, MINPACK, http://www.netlib.org:80/minpack/.
[8] Mysovskikh, I.P., Interpolatory cubature formulas, (1981), Izdat. Nauka, Moscow Leningrad, (Russian) · Zbl 0537.65019
[9] Radon, J., Zur mechanischen kubatur, Monatsh. math., 52, 286-300, (1948) · Zbl 0031.31504
[10] Stroud, A.H., Approximate calculation of multiple integrals, (1971), Prentice-Hall Englewood Cliffs, NJ · Zbl 0379.65013
[11] Stroud, A.H.; Secrest, D., Gaussian quadrature formulas, (1966), Prentice-Hall Englewood Cliffs, NJ · Zbl 0156.17002
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