Cubature formulae of the fifteenth degree of accuracy for a hypersphere
type: Item
instance of: scholarly article
title: Cubature formulae of the fifteenth degree of accuracy for a hypersphere
zbMATH Open document ID: 0796.65019
published in: Computational Mathematics and Mathematical Physics
publication date: 1994-03-03T00:00:00Z
review text: Let \(S_{n-1}\) be the unit sphere in \(\mathbb{R}^ n\) and \(Q_ n\) be the hyperoctahedron with vertices at \(\{(p_ 1, \dots, p_ n)\): \(p_ j=0\) for \(j \neq i\), \(p_ i=1\) or \(p_ i=-1\}^ n_{i=1}\). The author considers the existence of a cubature formula on \(S_{n-1}\) which integrates exactly all polynomials of degree less than or equal to 15 and which are invariant under the group of all transformations of \(Q_ n\) into itself. The number of the free parmeters (nodes and coefficients) is equal to the number of the fundamental invariant polynomials (equal to 15). Tables with the nodes and coefficients are given for some small \(n\) \((n=8,9,10)\) for which the cubature formula exists.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 486850
zbMATH Keywords: hypersphere
zbMATH Keywords: algebraic degree of precision
zbMATH Keywords: cubature formula
author: Srebra B. Stoyanova
reviewed by: Borislav D. Bojanov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 486850