Constructing fully symmetric cubature formulae for the sphere

Heo, Sangwoo; Xu, Yuan

doi:10.1090/S0025-5718-00-01198-4

Constructing fully symmetric cubature formulae for the sphere
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by Sangwoo Heo and Yuan Xu;

Math. Comp. 70 (2001), 269-279

DOI: https://doi.org/10.1090/S0025-5718-00-01198-4

Published electronically: March 3, 2000

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Abstract:

We construct symmetric cubature formulae of degrees in the 13-39 range for the surface measure on the unit sphere. We exploit a recently published correspondence between cubature formulae on the sphere and on the triangle. Specifically, a fully symmetric cubature formula for the surface measure on the unit sphere corresponds to a symmetric cubature formula for the triangle with weight function $(u_{1}u_{2}u_{3})^{-1/2}$, where $u_{1}$, $u_{2}$, and $u_{3}$ are homogeneous coordinates.

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