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

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 $n \geq 100$.

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Publisher:
Unspecified
Publication date:
2012-08-01
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Local pid:
oai:eprints.maths.ox.ac.uk:1600
Deposit date:
2012-09-07