The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note
The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurat...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6694369 |
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| _version_ | 1832546065264410624 |
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| author | Juan Zhang Mei Sun Enran Hou Zhaoxing Ma |
| author_facet | Juan Zhang Mei Sun Enran Hou Zhaoxing Ma |
| author_sort | Juan Zhang |
| collection | DOAJ |
| description | The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost. |
| format | Article |
| id | doaj-art-6a9657f7b96840c8b28cf3fd0081fe33 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6a9657f7b96840c8b28cf3fd0081fe332025-02-03T07:24:01ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66943696694369The Quasi-Optimal Radial Basis Function Collocation Method: A Technical NoteJuan Zhang0Mei Sun1Enran Hou2Zhaoxing Ma3School of Computer Science and Technology, Huaibei Normal University, Huaibei 235000, ChinaSchool of Computer Science and Technology, Huaibei Normal University, Huaibei 235000, ChinaSchool of Computer Science and Technology, Huaibei Normal University, Huaibei 235000, ChinaSchool of Information and Control Engineering, Qingdao University of Technology, Qingdao 273400, ChinaThe traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost.http://dx.doi.org/10.1155/2021/6694369 |
| spellingShingle | Juan Zhang Mei Sun Enran Hou Zhaoxing Ma The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note Journal of Mathematics |
| title | The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note |
| title_full | The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note |
| title_fullStr | The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note |
| title_full_unstemmed | The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note |
| title_short | The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note |
| title_sort | quasi optimal radial basis function collocation method a technical note |
| url | http://dx.doi.org/10.1155/2021/6694369 |
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