Numerical integration using sparse grids
type: Item
instance of: scholarly article
title: Numerical integration using sparse grids
zbMATH Open document ID: 0921.65022
DOI: 10.1023/A:1019129717644
author: Thomas Gerstner
author: Michael Griebel
published in: Numerical Algorithms
publication date: 1999-09-29T00:00:00Z
review text: The authors consider various constructions for multivariate quadrature formulas on sparse grids based on Newton-Cotes, Clenshaw-Curtis, Gauss and extended Gauss formulas. They present known results concerning the computational cost and error bounds and indicate a numerically stable implementation. A generalization of \textit{S. A. Smolyak}'s construction [Dokl. Akad. Nauk SSSR 148, 1042-1045 (1963; Zbl 0202.39901)] which can take into account the smoothness properties of the integrand varying with the dimension is given. Using a comparison of various univariate basic integration routines they show that nested quadrature formulas are the best choice for Smolyak's construction. The work contains a bibliography including 56 references from the most significant works in this domain.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 1268407
zbMATH Keywords: cubature formulas
zbMATH Keywords: complexity
zbMATH Keywords: Newton-Cotes formula
zbMATH Keywords: Clenshow-Curtis formula
zbMATH Keywords: multivariate quadrature formulas
zbMATH Keywords: sparse grids
zbMATH Keywords: extended Gauss formulas
zbMATH Keywords: error bounds
zbMATH Keywords: bibliography
reviewed by: Dumitru Acu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1268407