Year: 2011
Author: Qian Zhan, Shusheng Xu
Communications in Mathematical Research , Vol. 27 (2011), Iss. 3 : pp. 193–199
Abstract
The approximation of $|x|$ by rational functions is a classical rational problem. This paper deals with the rational approximation of the function $x^α$sgn$x$, which equals $|x|$ if $α = 1$. We construct a Newman type operator $r_n(x)$ and show $$\mathop{\rm min}\limits_{|x|≤1} \{|x^α{\rm sgn}x − r_n(x)| \} ∼ Cn^{−\frac{α}{2}}e^{−\sqrt{2nα}},$$ where $C$ is a constant depending on $α$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-CMR-19082
Communications in Mathematical Research , Vol. 27 (2011), Iss. 3 : pp. 193–199
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 7
Keywords: rational approximation asymptotic property Newman type operator.