On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules
Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, together with the efficient evaluation of the modified moments by forward recursions or by Oliver’s algorithms, this paper presents fast and stable interpolating integration algorith...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/436164 |
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| _version_ | 1832565353891233792 |
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| author | Shuhuang Xiang Guo He Haiyong Wang |
| author_facet | Shuhuang Xiang Guo He Haiyong Wang |
| author_sort | Shuhuang Xiang |
| collection | DOAJ |
| description | Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, together with the efficient evaluation of the modified moments by forward recursions or by Oliver’s algorithms, this paper presents fast and stable interpolating integration algorithms, by using the coefficients and modified moments, for Clenshaw-Curtis, Fejér’s first- and second-type rules for Jacobi weights or Jacobi weights multiplied by a logarithmic function. Numerical examples illustrate the stability, efficiency, and accuracy of these quadratures. |
| format | Article |
| id | doaj-art-18693cd532cb404fa61ca6a616fea83a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-18693cd532cb404fa61ca6a616fea83a2025-02-03T01:07:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/436164436164On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature RulesShuhuang Xiang0Guo He1Haiyong Wang2School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, ChinaBased upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, together with the efficient evaluation of the modified moments by forward recursions or by Oliver’s algorithms, this paper presents fast and stable interpolating integration algorithms, by using the coefficients and modified moments, for Clenshaw-Curtis, Fejér’s first- and second-type rules for Jacobi weights or Jacobi weights multiplied by a logarithmic function. Numerical examples illustrate the stability, efficiency, and accuracy of these quadratures.http://dx.doi.org/10.1155/2014/436164 |
| spellingShingle | Shuhuang Xiang Guo He Haiyong Wang On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules Abstract and Applied Analysis |
| title | On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules |
| title_full | On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules |
| title_fullStr | On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules |
| title_full_unstemmed | On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules |
| title_short | On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules |
| title_sort | on fast and stable implementation of clenshaw curtis and fejer type quadrature rules |
| url | http://dx.doi.org/10.1155/2014/436164 |
| work_keys_str_mv | AT shuhuangxiang onfastandstableimplementationofclenshawcurtisandfejertypequadraturerules AT guohe onfastandstableimplementationofclenshawcurtisandfejertypequadraturerules AT haiyongwang onfastandstableimplementationofclenshawcurtisandfejertypequadraturerules |