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：

中国国家自然科学基金; 北京市自然科学基金;

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

共 16 条

[1] Hyperinterpolation in the cube [J].

Caliari, Marco ;

De Marchi, Stefano ;

Vianello, Marco .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 55 (11) :2490-2497

[2] Hyperinterpolation on the square [J].

Caliari, Marco ;

De Marchi, Stefano ;

Vianello, Marco .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 210 (1-2) :78-83

[3] Hyper2d: A numerical code for hyperinterpolation on rectangles [J].

Caliari, Marco ;

Vianello, Marco ;

De Marchi, Stefano ;

Montagna, Roberto .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 183 (02) :1138-1147

[4] On generalized hyperinterpolation on the sphere [J].

Dai, Feng .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (10) :2931-2941

[5] New cubature formulae and hyperinterpolation in three variables [J].

De Marchi, Stefano ;

Vianello, Marco ;

Xu, Yuan .

BIT NUMERICAL MATHEMATICS, 2009, 49 (01) :55-73

[6] On the norm of the hyperinterpolation operator on the unit disc and its use for the solution of the nonlinear Poisson equation [J].

Hansen, Olaf ;

Atkinson, Kendall ;

Chien, David .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2009, 29 (02) :257-283

[7]

HESSE K., 2006, Frontiers in Interpolation and Approximation (Dedicated to the Memory of Ambikeshwar Sharma), P213

[8] The uniform norm of hyperinterpolation on the unit sphere in an arbitrary number of dimensions [J].

Le Gia, T ;

Sloan, IH .

CONSTRUCTIVE APPROXIMATION, 2001, 17 (02) :249-265

[9] Generalized hyperinterpolation on the sphere and the Newman-Shapiro operators [J].

Reimer, M .

CONSTRUCTIVE APPROXIMATION, 2002, 18 (02) :183-203

[10] Hyperinterpolation on the sphere at the minimal projection order [J].

Reimer, M .

JOURNAL OF APPROXIMATION THEORY, 2000, 104 (02) :272-286

← 1 2 →