Simple cubature formulas with high polynomial exactness
type: Item
instance of: scholarly article
title: Simple cubature formulas with high polynomial exactness
zbMATH Open document ID: 0942.41018
author: Klaus Ritter
author: Erich Novak
published in: Constructive Approximation
publication date: 2000-08-17T00:00:00Z
review text: The authors study cubature formulas for \(d\)-dimensional integrals with arbitrary weight function of tensor product form. They construct formulas that yield a high polynomial exactness. If the degree of accuracy is fixed then the number of knots depends on the dimension in an order-optimal way. They derived cubature formulae which are universal, that means that the order of convergence is almost optimal for two different scales of function spaces. The construction is simple because only a small number of arithmetical operations is needed to compute the knots and the weights of the formulae.
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1398359
zbMATH Keywords: cubature formula
zbMATH Keywords: polynomial exactness
zbMATH Keywords: universality
zbMATH Keywords: optimal error bounds
zbMATH Keywords: fully symmetric formula
zbMATH Keywords: sparse grids
zbMATH Keywords: interpolation
reviewed by: Josef Kofroň
describes a project that uses: HRMSYM
describes a project that uses: PATSYM
MaRDI profile type: Publication
full work available at URL: s003659900119
OpenAlex ID: W2103455761
Wikidata QID: Q126988103
DOI: 10.1007/S003659900119
description: scientific article; zbMATH DE number 1398359