Spherical quasi-interpolation using scaled zonal kernels
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916916801568768 |
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| author | Sun, Zhengjie Gao, Wenwu Sun, Xingping |
| author_facet | Sun, Zhengjie Gao, Wenwu Sun, Xingping |
| contents | We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson kernel, Gaussian, compactly-supported radial kernels), so that the underlying spherical convolution operators (upon the introduction of a scaling parameter) attains a high-order of approximation to target functions. In Phase II, we discretize the spherical integrals utilizing quadrature rules of optimal order to produce the final quasi-interpolants. Numerical experiments demonstrate that the new quasi-interpolation algorithm is robust and amenable to integrated as well as distributed ways of implementation. Moreover, the underlying error-analysis shows that by fine-tuning the scaling parameter in the radial kernels employed, the resulting quasi-interpolants achieve a well-balanced trade-off between approximation and sampling errors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14803 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spherical quasi-interpolation using scaled zonal kernels Sun, Zhengjie Gao, Wenwu Sun, Xingping Numerical Analysis 43A90, 41A25, 41A55, 65D12, 65D32 We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson kernel, Gaussian, compactly-supported radial kernels), so that the underlying spherical convolution operators (upon the introduction of a scaling parameter) attains a high-order of approximation to target functions. In Phase II, we discretize the spherical integrals utilizing quadrature rules of optimal order to produce the final quasi-interpolants. Numerical experiments demonstrate that the new quasi-interpolation algorithm is robust and amenable to integrated as well as distributed ways of implementation. Moreover, the underlying error-analysis shows that by fine-tuning the scaling parameter in the radial kernels employed, the resulting quasi-interpolants achieve a well-balanced trade-off between approximation and sampling errors. |
| title | Spherical quasi-interpolation using scaled zonal kernels |
| topic | Numerical Analysis 43A90, 41A25, 41A55, 65D12, 65D32 |
| url | https://arxiv.org/abs/2408.14803 |