Fully symmetric interpolatory rules for multiple integrals over hyper-spherical surfaces

Authors:
Alan Genz
Affiliations:
Department of Mathematics, Washington State University, Pullman, WA
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

Fully symmetric interpolatory integration rules are constructed for multidimensional integrals over Un, the surface of an n-dimensional hyper-sphere. Explicit formulas for the weights are given for odd degrees 3-13. The new rules are efficient and only moderately unstable. Two randomization methods are described.