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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 , where , , and 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