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Constructing fully symmetric cubature formulae for the sphere


Authors: Sangwoo Heo and Yuan Xu
Journal: Math. Comp. 70 (2001), 269-279
MSC (2000): Primary 65D32, 41A55, 41A63
DOI: https://doi.org/10.1090/S0025-5718-00-01198-4
Published electronically: March 3, 2000
MathSciNet review: 1680883
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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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Additional Information

Sangwoo Heo
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
Email: yuan@math.uoregon.edu

Yuan Xu
Affiliation: Division of Science and Mathematics, University of Minnesota-Morris, Morris, Minnesota 56267
Address at time of publication: Department of Mathematics, University of Southern Indiana, Evansville, Indiana 47712
Email: sheo@cda.mrs.umn.edu

DOI: https://doi.org/10.1090/S0025-5718-00-01198-4
Keywords: Cubature formulae, on the unit sphere, on the triangle, symmetric formula on a triangle, octahedral symmetry
Received by editor(s): July 8, 1997
Received by editor(s) in revised form: February 6, 1998, July 14, 1998, and January 12, 1999
Published electronically: March 3, 2000
Additional Notes: Supported by the National Science Foundation under Grants DMS-9500532 and 9802265.
Article copyright: © Copyright 2000 American Mathematical Society