Volume 31, Issue 2
Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting

Z. X. Huang & H. P. Wang

Anal. Theory Appl., 31 (2015), pp. 154-166.

Published online: 2017-04

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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 $L_q({\mathbb{S}^{d-1}})$ metric for $1\le q\le \infty$, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the $L_q(\mathbb{S}^{d-1})$ metric for $1\le q\le \infty$.

  • Keywords

Optimal recovery on the sphere, average sampling numbers, optimal algorithm, Gaussian measure.

  • AMS Subject Headings

41A25, 41A35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-31-154, author = {}, title = {Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {2}, pages = {154--166}, 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 $L_q({\mathbb{S}^{d-1}})$ metric for $1\le q\le \infty$, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the $L_q(\mathbb{S}^{d-1})$ metric for $1\le q\le \infty$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n2.5}, url = {http://global-sci.org/intro/article_detail/ata/4630.html} }
TY - JOUR T1 - Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting JO - Analysis in Theory and Applications VL - 2 SP - 154 EP - 166 PY - 2017 DA - 2017/04 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n2.5 UR - https://global-sci.org/intro/article_detail/ata/4630.html KW - Optimal recovery on the sphere, average sampling numbers, optimal algorithm, Gaussian measure. AB -

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 $L_q({\mathbb{S}^{d-1}})$ metric for $1\le q\le \infty$, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the $L_q(\mathbb{S}^{d-1})$ metric for $1\le q\le \infty$.

Z. X. Huang & H. P. Wang. (1970). Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting. Analysis in Theory and Applications. 31 (2). 154-166. doi:10.4208/ata.2015.v31.n2.5
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