Numerical integration formulas of degree two

Authors:
Dongbin Xiu
Affiliations:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 4
Cited 2

Monomial cubature rules since “Stroud”: a compilation

Journal of Computational and Applied Mathematics
Monomial cubature rules since “Stroud”: a compilation—part 2

Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
My dream quadrature rule

Journal of Complexity
An encyclopaedia of cubature formulas

Journal of Complexity

Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty

Applied Numerical Mathematics
Adaptive approximation of higher order posterior statistics

Journal of Computational Physics

Quantified Score

Hi-index	0.01

Visualization

Abstract

Numerical integration formulas in n-dimensional nonsymmetric Euclidean space of degree two, consisting of n+1 equally weighted points, are discussed, for a class of integrals often encountered in statistics. This is an extension of Stroud's theory [A.H. Stroud, Remarks on the disposition of points in numerical integration formulas, Math. Comput. 11 (60) (1957) 257-261; A.H. Stroud, Numerical integration formulas of degree two, Math. Comput. 14 (69) (1960) 21-26]. Explicit formulas are given for integrals with nonsymmetric weights. These appear to be new results and include the Stroud's degree two formula as a special case.