Constructing cubature formulae for spheres and balls
type: Item
instance of: scholarly article
title: Constructing cubature formulae for spheres and balls
zbMATH Open document ID: 0941.65017
DOI: 10.1016/S0377-0427(99)00216-2
author: Sangwoo Heo
author: Yuan Xu
published in: Journal of Computational and Applied Mathematics
publication date: 2000-07-20T00:00:00Z
review text: The purpose of this paper is to use the correspondence on the sphere [cf. \textit{Y. Xu}, SIAM J. Math. Anal. 29, No.~3, 779-793 (1998; Zbl 0907.33005)] on the sphere. Also, using this correspondence, a number of cubature formulae for the Chebyshev weight function on the ball \(B(2)\) follows from the formulae for the surface measure on the sphere \(S(2)\). The authors devote their main effort to the construction of cubature formulae with respect to the Chebyshev weight function on \(B(2)\). These formulae that are different from the ones obtained from the correspondence will lead to new cubature formulate for the Lebesgue measure on the sphere. Several numerical examples are given.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 1398800
zbMATH Keywords: cubature formulae
zbMATH Keywords: sphere
zbMATH Keywords: Chebyshev weight function
zbMATH Keywords: numerical examples
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1398800