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

Nicholas Hale; Alex Townsend

doi:10.1137/120889873

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

Nicholas Hale, Alex Townsend

Research output: Contribution to journal › Article › peer-review

139 Scopus citations

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.

Original language	English (US)
Pages (from-to)	A652-A674
Number of pages	1
Journal	SIAM Journal on Scientific Computing
Volume	35
Issue number	2
DOIs	https://doi.org/10.1137/120889873
State	Published - Mar 6 2013
Externally published	Yes

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title = "Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights",

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. {\textcopyright} 2013 Society for Industrial and Applied Mathematics.",

author = "Nicholas Hale and Alex Townsend",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This work was supported by The MathWorks, Inc., and King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2013",

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doi = "10.1137/120889873",

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T1 - Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights

AU - Hale, Nicholas

AU - Townsend, Alex

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This work was supported by The MathWorks, Inc., and King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013/3/6

Y1 - 2013/3/6

N2 - 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.

AB - 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.

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JO - SIAM Journal on Scientific Computing

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ER -

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

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