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Constructing cubature formulae for spheres and balls

โœ Scribed by Sangwoo Heo; Yuan Xu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
149 KB
Volume
112
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

It has been shown recently that cubature formulae for the unit sphere and for the unit ball are closely related; in particular, cubature formulae for the surface measure on the sphere correspond to formulae for the Chebyshev weight function on the ball. This provides a new method to generate cubature formulae on these regions. In this paper we construct a number of cubature formulae for the Chebyshev weight function on the unit ball in R 2 , and use them to derive new formulae for the surface measure on the sphere S 2 .

๐Ÿ“œ SIMILAR VOLUMES

Effectiveness for Embedded Spheres and B
Effectiveness for Embedded Spheres and Balls
โœ Joseph S. Miller ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 179 KB

We consider arbitrary dimensional spheres and closed balls embedded in R n as ฮ  0 1 classes. Such a strong restriction on the topology of a ฮ  0 1 class has computability theoretic repercussions. Algebraic topology plays a crucial role in our exploration of these consequences; the use of homology cha