Proceedings of the Workshop on Computation: Theory and Practice (WCTP 2024)

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Computing 32-Place Tables of Zeroes and Weights for Gauss-Legendre Quadrature

Authors
Pablo Manalastas1, *
1Retired faculty, Department of Information Systems & Computer Science, Ateneo de Manila University, Quezon City, Philippines
*Corresponding author. Email: pmanalastas@gmail.com
Corresponding Author
Pablo Manalastas
Available Online 30 April 2025.
DOI
10.2991/978-94-6463-684-0_10How to use a DOI?
Keywords
Legendre polynomials; Gaussian quadrature; Newton’s method
Abstract

We numerically compute tables of zeroes and weights of Legendre polynomials Pn(x) correct to thirty-two decimal places for n = 2, 3, 4, …, 10, 12, 16, 20, 24, 32, 40, 48, 64, 80, and 96. These zeroes and weights are useful in Gaussian quadrature of arbitrary continuous functions over finite intervals. We compute the zeroes of Pn(x) by applying Newton’s method to the equation Pn(x) = 0. For Newton’s method, Pn(x) is computed using a nonrecursive C function using a for-loop. Then we compute the weights wi associated with each zero xi of Pn(x). All computations were done using gcc on an Intel x86 64 Linux laptop, using the quadmath library, in which the --float128 data type provides 35-digit precision equivalent to true long double.

Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the Workshop on Computation: Theory and Practice (WCTP 2024)
Series
Atlantis Highlights in Computer Sciences
Publication Date
30 April 2025
ISBN
978-94-6463-684-0
ISSN
2589-4900
DOI
10.2991/978-94-6463-684-0_10How to use a DOI?
Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Pablo Manalastas
PY  - 2025
DA  - 2025/04/30
TI  - Computing 32-Place Tables of Zeroes and Weights for Gauss-Legendre Quadrature
BT  - Proceedings of the  Workshop on Computation: Theory and Practice (WCTP 2024)
PB  - Atlantis Press
SP  - 151
EP  - 166
SN  - 2589-4900
UR  - https://doi.org/10.2991/978-94-6463-684-0_10
DO  - 10.2991/978-94-6463-684-0_10
ID  - Manalastas2025
ER  -