Asymptotic Property of Approximation to xαsgn x by Newman Type Operators

Approximation to the function ｜x｜ plays an important role in approximation theory. This paper studies the approximation to the function xαsgn x, which equals ｜x｜ if α = 1. We construct a Newman Type Operator rn（x） and prove max ｜x｜≤1｜xαsgn x-rn（x）｜～Cn1/4e-π1/2（1/2）αn....

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2010-10, Vol.26 (4), p.617-624
Main Authors: Zhan, Qian, Xu, Shu-sheng, Zhang, Yue-hong
Format: Article
Language:English
Subjects:
an型
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
函数逼近
渐近性质
胡志明市
逼近函数
逼近理论
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Summary:Approximation to the function ｜x｜ plays an important role in approximation theory. This paper studies the approximation to the function xαsgn x, which equals ｜x｜ if α = 1. We construct a Newman Type Operator rn（x） and prove max ｜x｜≤1｜xαsgn x-rn（x）｜～Cn1/4e-π1/2（1/2）αn.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-007-7147-x