Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting |
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| Authors: | Zexia Huang Heping Wang |
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| Affiliation: | 1. School of Science, Xihua University, Chengdu 610039, China;2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China |
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| Abstract: | In this paper, we study optimal recovery (reconstruction) of functions on the sphere in the average case setting.We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq(Sd?1) metric for 1≤q≤∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq(Sd?1) metric for 1≤q≤∞. |
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| Keywords: | Optimal recovery on the sphere average sampling numbers optimal algorithm Gaussian measure |
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