Optimal recovery of isotropic classes of twice-differentiable functions defined on d-dimensional Euclidean space

JOURNAL OF APPROXIMATION THEORY

卷:182

Article

Ling, Bo¹  Liu, Yongping¹ 

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

关键词: Optimal recovery;    Differentiable function;    Optimal covering;    Discrete geometry;   

DOI  :  10.1016/j.jat.2014.03.005

来源: Elsevier

【 摘 要 】

In the paper, inspired by the works of V. F. Babenko, S. V. Borodachov and D. S. Skorokhodov, we consider the problem of optimal recovery of isotropic classes of twice-differentiable multivariate functions defined on Euclidean space R-d, and get some exact results. This problem is connected with the optimal covering of Rd in discrete geometry. What Babenko et al. considered is the same kind of the optimal recovery problem of an isotropic class of twice-differentiable multivariate functions defined on a compact set of R-d and an isotropic class of twice-differentiable periodic functions. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free