Accurate Evaluation of Polynomials in Legendre Basis
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 coe...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/742538 |
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| _version_ | 1832553083135066112 |
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| author | Peibing Du Hao Jiang Lizhi Cheng |
| author_facet | Peibing Du Hao Jiang Lizhi Cheng |
| author_sort | Peibing Du |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b881806b11c74617951c3dc4ee62ea54 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b881806b11c74617951c3dc4ee62ea542025-02-03T05:57:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/742538742538Accurate Evaluation of Polynomials in Legendre BasisPeibing Du0Hao Jiang1Lizhi Cheng2Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, ChinaThe State Key Laboratory for High Performance Computation, College of Computer Science, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, ChinaThis 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.http://dx.doi.org/10.1155/2014/742538 |
| spellingShingle | Peibing Du Hao Jiang Lizhi Cheng Accurate Evaluation of Polynomials in Legendre Basis Journal of Applied Mathematics |
| title | Accurate Evaluation of Polynomials in Legendre Basis |
| title_full | Accurate Evaluation of Polynomials in Legendre Basis |
| title_fullStr | Accurate Evaluation of Polynomials in Legendre Basis |
| title_full_unstemmed | Accurate Evaluation of Polynomials in Legendre Basis |
| title_short | Accurate Evaluation of Polynomials in Legendre Basis |
| title_sort | accurate evaluation of polynomials in legendre basis |
| url | http://dx.doi.org/10.1155/2014/742538 |
| work_keys_str_mv | AT peibingdu accurateevaluationofpolynomialsinlegendrebasis AT haojiang accurateevaluationofpolynomialsinlegendrebasis AT lizhicheng accurateevaluationofpolynomialsinlegendrebasis |