Extremal systems of points and numerical integration on the sphere
type: Item
instance of: scholarly article
title: Extremal systems of points and numerical integration on the sphere
zbMATH Open document ID: 1055.65038
author: Ian H. Sloan
author: Robert S. Womersley
published in: Advances in Computational Mathematics
publication date: 2004-05-27T00:00:00Z
review text: The purpose of this paper is to study certain results concerning the extremal systems of points on the unit sphere \(S^r\subseteq \mathbb{R}^{r+1}\), related to problems of numerical integration and geometrical properties of extremal systems. The authors consider the worst case cubature error in a certain Hilbert space and its relation to a generalized discrepancy. The minimum geodesic distance between pairs of points and the mesh norm are discussed. They also consider numerical examples.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 2069020
zbMATH Keywords: points on the sphere
zbMATH Keywords: extremal systems
zbMATH Keywords: cubature rule
zbMATH Keywords: worst-case error
zbMATH Keywords: generalized discrepancy
zbMATH Keywords: numerical examples
reviewed by: Dumitru Acu
MaRDI profile type: Publication
DOI: 10.1023/B:ACOM.0000016428.25905.DA
description: scientific article; zbMATH DE number 2069020