Sampling numbers of a class of infinitely differentiable functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Wang, Heping¹  Xu, Guiqiao² 

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

[2] Tianjin Normal Univ, Dept Math, Tianjin 300387, Peoples R China

关键词: Sampling numbers;    Optimal algorithm;    Lagrange interpolation;   

DOI  :  10.1016/j.jmaa.2019.123689

来源: Elsevier

【 摘 要 】

This paper investigates the optimal recovery of a class Fm of infinitely differentiable functions on [ LI.] in L,[-1,1]. We obtain strong equivalences of the sampling numbers of Foo in L,[-1,1], 1 < p < oo, and even equality in L0.0[-1, 1]. We prove that the Lagrange interpolation algorithms k, 1 < p < oo, based on the zeros of the polynomial of degree n with the leading coefficient 1 of the least deviation from zero in L0[-1, 1] are strongly asymptotically optimal for 1 < p < co, and optimal for p = oo. 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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