Accurate Evaluation of Polynomials in Legendre Basis
Joint Authors
Du, Peibing
Jiang, Hao
Cheng, Li-Zhi
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-23
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Du, Peibing& Jiang, Hao& Cheng, Li-Zhi. 2014. Accurate Evaluation of Polynomials in Legendre Basis. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-495154
Modern Language Association (MLA)
Du, Peibing…[et al.]. Accurate Evaluation of Polynomials in Legendre Basis. Journal of Applied Mathematics No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-495154
American Medical Association (AMA)
Du, Peibing& Jiang, Hao& Cheng, Li-Zhi. Accurate Evaluation of Polynomials in Legendre Basis. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-495154
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-495154