On the Smolyak cubature error for analytic functions
type: Item
instance of: scholarly article
title: On the Smolyak cubature error for analytic functions
zbMATH Open document ID: 0947.65024
DOI: 10.1023/A:1018904816230
author: Knut Petras
published in: Advances in Computational Mathematics
publication date: 2000-03-21T00:00:00Z
review text: The author examines the Smolyak cubature error for analytic functions in the Cartesian product of ellipses. Kronrod-Patterson quadrature formulae are proposed as the corresponding basic sequence and this choice is compared with Clenshaw-Curtis quadrature formulae. First, he calculates error bounds for the one-dimensional case, which lead by a recursion formula to error bounds for higher-dimensional integration. Finally, the author gives some numerical examples.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 1419499
zbMATH Keywords: cubature
zbMATH Keywords: Smolyak algorithm
zbMATH Keywords: error bounds
zbMATH Keywords: analytic functions
zbMATH Keywords: Clenshaw-Curtis quadrature
zbMATH Keywords: Kronrod-Patterson quadrature
zbMATH Keywords: numerical examples
reviewed by: Dumitru Acu
MaRDI profile type: Publication
full work available at URL: a:1018904816230
OpenAlex ID: W1560266390
description: scientific article; zbMATH DE number 1419499