On the norm of the hyperinterpolation operator on the d-dimensional cube

被引：13

作者：

Wang, Heping ^{[1
]}

Wang, Kai ^{[2
]}

Wang, Xiaoli ^{[2
]}

机构：

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

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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 68卷 / 05期

基金：

北京市自然科学基金; 中国国家自然科学基金;

关键词：

Hyperinterpolation; Operator norm; Projection; Regular condition; GENERALIZED HYPERINTERPOLATION; APPROXIMATION; SPHERE;

D O I：

10.1016/j.camwa.2014.07.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain the asymptotic order of the operator norm of the hyperinterpolation operator on the cube I-d = [-1, 1](d), d >= 2 with respect to the measure d mu(x) = Pi(d)(i=1) dx(i)/pi root 1-x(i)(2). This gives an affirmative answer to a conjecture raised by Caliari et al. (2008). (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：632 / 638

页数：7

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