Open Access
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


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.


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Peibing Du. Hao Jiang. Lizhi Cheng. "Accurate Evaluation of Polynomials in Legendre Basis." J. Appl. Math. 2014 1 - 13, 2014.


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

Vol.2014 • 2014
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