Strong Inequalities for Hermite-Fejér Interpolations and Characterization of K-Functionals
The works of Smale and Zhou (2003, 2007), Cucker and Smale (2002), and Cucker and Zhou (2007) indicate that approximation operators serve as cores of many machine learning algorithms. In this paper we study the Hermite-Fejér interpolation operator which has this potential of applications. The interp...
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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/10.1155/2014/781068 |
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| author | Gongqiang You |
| author_facet | Gongqiang You |
| author_sort | Gongqiang You |
| collection | DOAJ |
| description | The works of Smale and Zhou (2003, 2007), Cucker and Smale (2002), and Cucker and Zhou (2007) indicate that approximation operators serve as cores of many machine learning algorithms. In this paper we study the Hermite-Fejér interpolation operator which has this potential of
applications. The interpolation is defined by zeros of the Jacobi polynomials with parameters −1<α, β<0. Approximation rate is obtained for continuous functions. Asymptotic expression of the K-functional associated with the interpolation operators is given. |
| format | Article |
| id | doaj-art-2e661de2d0e34464b17ea3483fd8789a |
| 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-2e661de2d0e34464b17ea3483fd8789a2025-08-20T03:55:07ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/781068781068Strong Inequalities for Hermite-Fejér Interpolations and Characterization of K-FunctionalsGongqiang You0Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, ChinaThe works of Smale and Zhou (2003, 2007), Cucker and Smale (2002), and Cucker and Zhou (2007) indicate that approximation operators serve as cores of many machine learning algorithms. In this paper we study the Hermite-Fejér interpolation operator which has this potential of applications. The interpolation is defined by zeros of the Jacobi polynomials with parameters −1<α, β<0. Approximation rate is obtained for continuous functions. Asymptotic expression of the K-functional associated with the interpolation operators is given.http://dx.doi.org/10.1155/2014/781068 |
| spellingShingle | Gongqiang You Strong Inequalities for Hermite-Fejér Interpolations and Characterization of K-Functionals Abstract and Applied Analysis |
| title | Strong Inequalities for Hermite-Fejér Interpolations and Characterization of K-Functionals |
| title_full | Strong Inequalities for Hermite-Fejér Interpolations and Characterization of K-Functionals |
| title_fullStr | Strong Inequalities for Hermite-Fejér Interpolations and Characterization of K-Functionals |
| title_full_unstemmed | Strong Inequalities for Hermite-Fejér Interpolations and Characterization of K-Functionals |
| title_short | Strong Inequalities for Hermite-Fejér Interpolations and Characterization of K-Functionals |
| title_sort | strong inequalities for hermite fejer interpolations and characterization of k functionals |
| url | http://dx.doi.org/10.1155/2014/781068 |
| work_keys_str_mv | AT gongqiangyou stronginequalitiesforhermitefejerinterpolationsandcharacterizationofkfunctionals |