Scattered data quasi‐interpolation on spheres |
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| Authors: | Zhixiang Chen Feilong Cao Ming Li |
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| Affiliation: | 1. Department of Mathematics, Shaoxing University, Shaoxing 312000, Zhejiang Province, China;2. Department of Mathematics, China Jiliang University, Hangzhou 310018, Zhejiang Province, China |
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| Abstract: | This paper studies the construction and approximation of quasi‐interpolation for spherical scattered data. First of all, a kind of quasi‐interpolation operator with Gaussian kernel is constructed to approximate the spherical function, and two Jackson type theorems are established. Second, the classical Shepard operator is extended from Euclidean space to the unit sphere, and the error of approximation by the spherical Shepard operator is estimated. Finally, the compact supported kernel is used to construct quasi‐interpolation operator for fitting spherical scattered data, where the spherical modulus of continuity and separation distance of scattered sampling points are employed as the measurements of approximation error. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | spherical scattered data quasi‐interpolation spherical basis function approximation error |
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