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

Journal article

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.

Authors: Hale, N; Townsend, A

• Publication date: 2012-01-01