L p Error Estimates for Scattered Data Interpolation On Spheres |
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| Authors: | Feilong Cao Xiaofei Guo Shaobo Lin |
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| Affiliation: | 1. Department of Mathematics , China Jiliang University , Hangzhou, Zhejiang Province, P. R. China feilongcao@gmail.com;3. Department of Mathematics , China Jiliang University , Hangzhou, Zhejiang Province, P. R. China;4. Institute for Information and System Sciences , Xi'an Jiaotong University , Xi'an, Shannxi Province, P. R. China |
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| Abstract: | In this article, working with the sphere 𝕊 d embedded in the (d + 1)-dimensional Euclidean space ? d+1 as the underlying manifold, we obtain an error estimate for interpolating functions f ∈ H μ from shifts of a smooth positive definite function defined on 𝕊 d , where H μ is a Sobolev space. We also get an L p error estimate for f by using a method of Duchon framework. |
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| Keywords: | Interpolation L p error estimate Scattered data Sphere |
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