Complex generalized Gauss-Radau quadrature rules for Hankel transforms of integer order
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909556453408768 |
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| author | Wang, Haiyong Wu, Menghan |
| author_facet | Wang, Haiyong Wu, Menghan |
| contents | Complex Gaussian quadrature rules for oscillatory integral transforms have the advantage that they can achieve optimal asymptotic order. However, their existence for Hankel transform can only be guaranteed when the order of the transform belongs to $[0,1/2]$. In this paper we consider the construction of generalized Gauss-Radau quadrature rules for Hankel transform. We show that, if adding certain value and derivative information at the left endpoint, then complex generalized Gauss-Radau quadrature rules for Hankel transform of integer order can be constructed with theoretical guarantees. Orthogonal polynomials that are closely related to such quadrature rules are investigated and their existence for even degrees is proved. Numerical experiments are presented to confirm our findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complex generalized Gauss-Radau quadrature rules for Hankel transforms of integer order Wang, Haiyong Wu, Menghan Numerical Analysis Classical Analysis and ODEs 65R10, 65D32 Complex Gaussian quadrature rules for oscillatory integral transforms have the advantage that they can achieve optimal asymptotic order. However, their existence for Hankel transform can only be guaranteed when the order of the transform belongs to $[0,1/2]$. In this paper we consider the construction of generalized Gauss-Radau quadrature rules for Hankel transform. We show that, if adding certain value and derivative information at the left endpoint, then complex generalized Gauss-Radau quadrature rules for Hankel transform of integer order can be constructed with theoretical guarantees. Orthogonal polynomials that are closely related to such quadrature rules are investigated and their existence for even degrees is proved. Numerical experiments are presented to confirm our findings. |
| title | Complex generalized Gauss-Radau quadrature rules for Hankel transforms of integer order |
| topic | Numerical Analysis Classical Analysis and ODEs 65R10, 65D32 |
| url | https://arxiv.org/abs/2403.19328 |