Open Access
Translator Disclaimer
2014 Accurate Evaluation of Polynomials in Legendre Basis
Peibing Du, Hao Jiang, Lizhi Cheng
J. Appl. Math. 2014: 1-13 (2014). DOI: 10.1155/2014/742538

Abstract

This paper presents a compensated algorithm for accurate evaluation of a polynomial in Legendre basis. Since the coefficients of the evaluated polynomial are fractions, we propose to store these coefficients in two floating point numbers, such as double-double format, to reduce the effect of the coefficients’ perturbation. The proposed algorithm is obtained by applying error-free transformation to improve the Clenshaw algorithm. It can yield a full working precision accuracy for the ill-conditioned polynomial evaluation. Forward error analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm.

Citation

Download Citation

Peibing Du. Hao Jiang. Lizhi Cheng. "Accurate Evaluation of Polynomials in Legendre Basis." J. Appl. Math. 2014 1 - 13, 2014. https://doi.org/10.1155/2014/742538

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131838
MathSciNet: MR3246429
Digital Object Identifier: 10.1155/2014/742538

Rights: Copyright © 2014 Hindawi

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.2014 • 2014
Back to Top