Spherical Designs for Function Approximation and Beyond
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909059492347904 |
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| author | Xiao, Yuchen Zhuang, Xiaosheng |
| author_facet | Xiao, Yuchen Zhuang, Xiaosheng |
| contents | In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we investigate the approximation of smooth and non-smooth functions by spherical harmonics with spherical designs. Finally, we use spherical framelets for denoising Wendland functions as an application, which shows the great potential of spherical designs in spherical data processing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18333 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spherical Designs for Function Approximation and Beyond Xiao, Yuchen Zhuang, Xiaosheng Numerical Analysis Signal Processing 42C05, 58C35, 65K10, 65D15, 65D32 In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we investigate the approximation of smooth and non-smooth functions by spherical harmonics with spherical designs. Finally, we use spherical framelets for denoising Wendland functions as an application, which shows the great potential of spherical designs in spherical data processing. |
| title | Spherical Designs for Function Approximation and Beyond |
| topic | Numerical Analysis Signal Processing 42C05, 58C35, 65K10, 65D15, 65D32 |
| url | https://arxiv.org/abs/2311.18333 |