Stratified nested and related quadrature rules
type: Item
instance of: scholarly article
title: Stratified nested and related quadrature rules
zbMATH Open document ID: 0958.65029
DOI: 10.1016/S0377-0427(99)00224-1
published in: Journal of Computational and Applied Mathematics
publication date: 2001-03-28T00:00:00Z
review text: The author extends the stratified nested quadrature procedure due to \textit{D. P. Laurie} [Quaest. Math. 15, No.~3, 365-384 (1992; Zbl 0788.65025)] to the concept of hybrid GKP rules (optimal extension of the Gauss 1-point rule). The procedure of \textit{F. T. Krogh} and \textit{W. Van Snyder} [ACM Trans. Math. Softw. 17, No.~4, 457-461 (1991; Zbl 0900.65054)], the hybrid strategy and the rules of \textit{J. M. Perez-Jorda} and \textit{E. San-Fabian} [Comput. Phys. Commun. 77, No.~1-3, 46-56 (1993; Zbl 0854.65017)] are extensively investigated. Comparative performances analysis recommand GKP rules for automatic integration.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 1398809
zbMATH Keywords: quadrature rule
zbMATH Keywords: nested quadrature procedure
zbMATH Keywords: hybrid GKP rules
zbMATH Keywords: comparative performance analysis
author: Thomas N. L. Patterson
describes a project that uses: ORTHPOL
describes a project that uses: Algorithm 699
describes a project that uses: Algorithm 719
MaRDI profile type: Publication
cites work: Algorithm 719: Multiprecision translation and execution of FORTRAN programs
cites work: A Fortran 90-based multiprecision system
cites work: Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules
cites work: Algorithm 699: a new representation of Patterson's quadrature formulae
cites work: STRATIFIED SEQUENCES OF NESTED QUADRATURE FORMULAS
cites work: The Optimum Addition of Points to Quadrature Formulae
cites work: An algorithm for generating interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions
cites work: A simple, efficient and more reliable scheme for automatic numerical integration
description: scientific article; zbMATH DE number 1398809