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Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights

By Nicholas Hale and Alex Townsend


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 $n \geq 100$

Topics: Special functions, Approximations and expansions, Numerical analysis
Publisher: Unspecified
Year: 2012
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