Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
KAUST Grant NumberKUK-C1-013-04
Online Publication Date2013-03-06
Print Publication Date2013-01
Permanent link to this recordhttp://hdl.handle.net/10754/598313
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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.
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.
SponsorsThis work was supported by The MathWorks, Inc., and King Abdullah University of Science and Technology (KAUST), award KUK-C1-013-04.