Ueberhuber (1997, p. 71) and Krommer and Ueberhuber (1998, pp. 49 and 155-165) use the word "quadrature" to mean numerical
computation of a univariate integral, and "cubature"
to mean numerical computation of a multiple integral.
Cubature techniques available in the Wolfram Language include Monte Carlo integration,
implemented as NIntegrate[f,
..., Method -> MonteCarlo] or NIntegrate[f,
..., Method -> QuasiMonteCarlo], and the adaptive Genz-Malik algorithm,
implemented as NIntegrate[f,
..., Method -> MultiDimensional].
Cools, R. "Monomial Cubature Rules Since "Stroud": A Compilation--Part 2." J. Comput. Appl. Math.112, 21-27, 1999.Cools,
R. "Encyclopaedia of Cubature Formulas." http://www.cs.kuleuven.ac.be/~nines/research/ecf/ecf.html.Cools,
R. "Constructing Cubature Formulae: The Science Behind the Art." In Acta
Numerica (Ed. A. Iserles). Cambridge, England: Cambridge University
Press, pp. 1-54, 1997.Cools, R. and Rabinowitz, P. "Monomial
Cubature Rules Since "Stroud": A Compilation." J. Comput. Appl.
Math.48, 309-326, 1993.Krommer, A. R. and Ueberhuber,
C. W. "Construction of Cubature Formulas." §6.1 in Computational
Integration. Philadelphia, PA: SIAM, pp. 155-165, 1998.Radon,
J. "Zur mechanische Kubatur." Monatsh. Math.42, 286-300,
1948.Ueberhuber, C. W. Numerical
Computation 2: Methods, Software, and Analysis. Berlin: Springer-Verlag,
1997.
