Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights

Handle URI:
http://hdl.handle.net/10754/598313
Title:
Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
Authors:
Hale, Nicholas; Townsend, Alex
Abstract:
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.
Citation:
Hale N, Townsend A (2013) Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights. SIAM Journal on Scientific Computing 35: A652–A674. Available: http://dx.doi.org/10.1137/120889873.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
6-Mar-2013
DOI:
10.1137/120889873
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This work was supported by The MathWorks, Inc., and King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorHale, Nicholasen
dc.contributor.authorTownsend, Alexen
dc.date.accessioned2016-02-25T13:18:31Zen
dc.date.available2016-02-25T13:18:31Zen
dc.date.issued2013-03-06en
dc.identifier.citationHale N, Townsend A (2013) Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights. SIAM Journal on Scientific Computing 35: A652–A674. Available: http://dx.doi.org/10.1137/120889873.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/120889873en
dc.identifier.urihttp://hdl.handle.net/10754/598313en
dc.description.abstractAn efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n ≥ 100. © 2013 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis work was supported by The MathWorks, Inc., and King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAsymptotic expansionen
dc.subjectGauss-Jacobien
dc.subjectGauss-Legendreen
dc.subjectQuadratureen
dc.titleFast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weightsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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