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Accurate Evaluation of Polynomials in Legendre Basis

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  • Peibing Du
  • Hao Jiang
  • Lizhi Cheng

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.

Suggested Citation

  • Peibing Du & Hao Jiang & Lizhi Cheng, 2014. "Accurate Evaluation of Polynomials in Legendre Basis," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-13, July.
    • Handle: RePEc:hin:jnljam:742538
    DOI: 10.1155/2014/742538
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    Cited by:

    1. Graillat, Stef, 2018. "An accurate algorithm for evaluating rational functions," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 494-503.

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