Iteration-free computation of Gauss-Legendre quadrature nodes and weights
- Author
- Ignace Bogaert (UGent)
- Organization
- Abstract
- Gauss-Legendre quadrature rules are of considerable theoretical and practical interest because of their role in numerical integration and interpolation. In this paper, a series expansion for the zeros of the Legendre polynomials is constructed. In addition, a series expansion useful for the computation of the Gauss-Legendre weights is derived. Together, these two expansions provide a practical and fast iteration-free method to compute individual Gauss-Legendre node-weight pairs in O(1) complexity and with double precision accuracy. An expansion for the barycentric interpolation weights for the Gauss-Legendre nodes is also derived. A C++ implementation is available online.
- Keywords
- BARYCENTRIC LAGRANGE INTERPOLATION, ALGORITHM, Legendre polynomial, parallel computing, asymptotic series, Gauss-Legendre quadrature
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-5683230
- MLA
- Bogaert, Ignace. “Iteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights.” SIAM JOURNAL ON SCIENTIFIC COMPUTING, vol. 36, no. 3, 2014, pp. A1008–26, doi:10.1137/140954969.
- APA
- Bogaert, I. (2014). Iteration-free computation of Gauss-Legendre quadrature nodes and weights. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 36(3), A1008–A1026. https://doi.org/10.1137/140954969
- Chicago author-date
- Bogaert, Ignace. 2014. “Iteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights.” SIAM JOURNAL ON SCIENTIFIC COMPUTING 36 (3): A1008–26. https://doi.org/10.1137/140954969.
- Chicago author-date (all authors)
- Bogaert, Ignace. 2014. “Iteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights.” SIAM JOURNAL ON SCIENTIFIC COMPUTING 36 (3): A1008–A1026. doi:10.1137/140954969.
- Vancouver
- 1.Bogaert I. Iteration-free computation of Gauss-Legendre quadrature nodes and weights. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 2014;36(3):A1008–26.
- IEEE
- [1]I. Bogaert, “Iteration-free computation of Gauss-Legendre quadrature nodes and weights,” SIAM JOURNAL ON SCIENTIFIC COMPUTING, vol. 36, no. 3, pp. A1008–A1026, 2014.
@article{5683230,
abstract = {{Gauss-Legendre quadrature rules are of considerable theoretical and practical interest because of their role in numerical integration and interpolation. In this paper, a series expansion for the zeros of the Legendre polynomials is constructed. In addition, a series expansion useful for the computation of the Gauss-Legendre weights is derived. Together, these two expansions provide a practical and fast iteration-free method to compute individual Gauss-Legendre node-weight pairs in O(1) complexity and with double precision accuracy. An expansion for the barycentric interpolation weights for the Gauss-Legendre nodes is also derived. A C++ implementation is available online.}},
author = {{Bogaert, Ignace}},
issn = {{1064-8275}},
journal = {{SIAM JOURNAL ON SCIENTIFIC COMPUTING}},
keywords = {{BARYCENTRIC LAGRANGE INTERPOLATION,ALGORITHM,Legendre polynomial,parallel computing,asymptotic series,Gauss-Legendre quadrature}},
language = {{eng}},
number = {{3}},
pages = {{A1008--A1026}},
title = {{Iteration-free computation of Gauss-Legendre quadrature nodes and weights}},
url = {{http://dx.doi.org/10.1137/140954969}},
volume = {{36}},
year = {{2014}},
}
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