accurate evaluation of polynomials in legendre basis
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ID: 168105
2014
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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.
| Reference Key |
du2014journalaccurate
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|---|---|
| Authors | ;Peibing Du;Hao Jiang;Lizhi Cheng |
| Journal | Chemico-biological interactions |
| Year | 2014 |
| DOI |
10.1155/2014/742538
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| URL | |
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