Accurate Evaluation of Polynomials in Legendre Basis | Zendy

Peibing Du | Zendy; Hao Jiang | Zendy; Lizhi Cheng | Zendy

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Accurate Evaluation of Polynomials in Legendre Basis

Author(s) -

Peibing Du,

Hao Jiang,

Lizhi Cheng

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/742538

Subject(s) - legendre polynomials , mathematics , polynomial , algorithm , approximation error , basis (linear algebra) , double precision floating point format , transformation (genetics) , wilkinson's polynomial , mathematical optimization , floating point , matrix polynomial , reciprocal polynomial , mathematical analysis , geometry , biochemistry , chemistry , gene

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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