Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
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- 1 January 2013
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 35 (2) , A652-A674
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 $\mathcal{O}(n)$ operations to an accuracy of essentially double precision for any $n\geq 100$.
Keywords
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