Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting  

作　　者：Zexia Huang Heping Wang 

机构地区：[1]School of Mathematical Sciences, Capital Normal University [2]School of Science, Xihua University

出　　处：《Analysis in Theory and Applications》2015年第2期154-166,共13页分析理论与应用（英文刊）

基　　金：supported by the National Natural Science Foundation of China(No.11426179);the National Natural Science Foundation of China(Nos.10871132,11271263);the Key Scientific Research Fund of Xihua University(No.z1312624);the Foundation of Sichuan Educational Committee(No.14ZA0112);the Preeminent Youth Fund for School of Science in Xihua University;the Beijing Natural Science Foundation(No.1132001);BCMIIS

摘　　要：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 （S^d-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 （S^d-1） metric for 1 ≤ q ≤ ∞.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 （S^d-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 （S^d-1） metric for 1 ≤ q ≤ ∞.

关 键 词：Optimal recovery on the sphere average sampling numbers optimal algorithm Gaussian measure. 

分 类 号：O224[理学—运筹学与控制论]