Monte Carlo quasi-interpolation of spherical data
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908591404875776 |
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| author | Sun, Zhengjie Lv, Mengyuan Sun, Xingping |
| author_facet | Sun, Zhengjie Lv, Mengyuan Sun, Xingping |
| contents | We establish a deterministic and stochastic spherical quasi-interpolation framework featuring scaled zonal kernels derived from radial basis functions on the ambient Euclidean space. The method incorporates both quasi-Monte Carlo and Monte Carlo quadrature rules to construct easily computable quasi-interpolants, which provide efficient approximation to Sobolev-space functions for both clean and noisy data. To enhance the approximation power and robustness of our quasi-interpolants, we develop a multilevel method in which quasi-interpolants constructed with graded resolutions join force to reduce the error of approximation. In addition, we derive probabilistic concentration inequalities for our quasi-interpolants in pertinent stochastic settings. The construction of our quasi-interpolants does not require solving any linear system of equations. Numerical experiments show that our quasi-interpolation algorithm is more stable and robust against noise than comparable ones in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12027 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monte Carlo quasi-interpolation of spherical data Sun, Zhengjie Lv, Mengyuan Sun, Xingping Numerical Analysis 43A90, 41A25, 41A55, 65D12, 65D32 We establish a deterministic and stochastic spherical quasi-interpolation framework featuring scaled zonal kernels derived from radial basis functions on the ambient Euclidean space. The method incorporates both quasi-Monte Carlo and Monte Carlo quadrature rules to construct easily computable quasi-interpolants, which provide efficient approximation to Sobolev-space functions for both clean and noisy data. To enhance the approximation power and robustness of our quasi-interpolants, we develop a multilevel method in which quasi-interpolants constructed with graded resolutions join force to reduce the error of approximation. In addition, we derive probabilistic concentration inequalities for our quasi-interpolants in pertinent stochastic settings. The construction of our quasi-interpolants does not require solving any linear system of equations. Numerical experiments show that our quasi-interpolation algorithm is more stable and robust against noise than comparable ones in the literature. |
| title | Monte Carlo quasi-interpolation of spherical data |
| topic | Numerical Analysis 43A90, 41A25, 41A55, 65D12, 65D32 |
| url | https://arxiv.org/abs/2510.12027 |