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.
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页码：632 / 638
页数：7
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