Sampling numbers of periodic Sobolev spaces with a Gaussian measure in the average case setting

JOURNAL OF APPROXIMATION THEORY

卷:167

Article

Huang, Zexia¹  Wang, Heping¹ 

[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

关键词: Average sampling numbers;    Standard information;    Optimal algorithm;    Gaussian measure;   

DOI  :  10.1016/j.jat.2012.11.010

来源: Elsevier

【 摘 要 】

In this paper, we investigate p-average sampling numbers of a periodic Sobolev space W-2(r) with a Gaussian measure in the L-q metric for 1 <= q <= infinity and 0 < p < infinity, and obtain their asymptotic orders. Moreover, we show that in the average case setting, the operators I-n, which are the Lagrange interpolating operators, are asymptotically optimal in the Lq metric for all 1 <= q <= infinity. It is interesting to note that in the worst case setting, In are not asymptotically optimal algorithms in the Lq metric for q = 1 or infinity. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free