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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 ≥ 100.

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A. Townsend More by this author
Publication date:
2012
URN:
uuid:f3363e49-c27a-4a8d-b911-26cd9055afd1
Local pid:
oai:eprints.maths.ox.ac.uk:1629

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