The Mathematical Institute, University of Oxford, Eprints Archive

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

Hale, Nicholas and Townsend, Alex (2012) Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights. Technical Report. Unspecified. (Submitted)

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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 $n \geq 100$.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Special functions
A - C > Approximations and expansions
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1600
Deposited By:Lotti Ekert
Deposited On:07 Sep 2012 08:39
Last Modified:07 Sep 2012 08:39

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