Reference: Nicholas Hale and Alex Townsend, (2012). Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights. Unspecified.Citable link to this page:
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 $n \geq 100$.