Accurate Evaluation of Polynomials in Legendre Basis

Peibing Du, Hao Jiang and Lizhi Cheng

Journal of Applied Mathematics, 2014, vol. 2014, 1-13

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:742538

DOI: 10.1155/2014/742538

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