Accurate Evaluation of Polynomials in Legendre Basis

Peibing Du, Hao Jiang and Lizhi Cheng

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/742538

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:742538

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