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

Nicholas Hale, Alex Townsend

Research output: Contribution to journalArticlepeer-review

89 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 languageEnglish (US)
Pages (from-to)A652-A674
Number of pages1
JournalSIAM Journal on Scientific Computing
Volume35
Issue number2
DOIs
StatePublished - Mar 6 2013
Externally publishedYes

Fingerprint

Dive into the research topics of 'Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights'. Together they form a unique fingerprint.

Cite this