Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2019, Vol. 36 ›› Issue (5): 551-556.doi: 10.3969/j.issn.1005-3085.2019.05.006

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The Rational Approximation to |x|α(1α<2) at the Adjusted Tangent Nodes

CHENG Yi-yuan1,  ZHANG Yong-quan2,  ZHA Xing-xing1   

  1. 1- School of Mathematics and Statistics, Chaohu College, Hefei 238000
    2- School of Data Sciences, Zhejiang University of Finance & Economics, Hangzhou 310018
  • Received:2017-06-13 Accepted:2018-05-08 Online:2019-10-15 Published:2019-12-15
  • Contact: Y. Zhang. E-mail address: zyqmath@163.com
  • Supported by:
    The National Natural Science Foundation of China (61573326); the Program in the Youth Elite Support Plan in Universities of Anhui Province (gxyq2019082); the First Class Discipline of Zhejiang-A (Zhejiang University of Finance and Economics-Statistics).

Abstract: Since Newman's rational operator has a good approximation for |x|, we consider the approximation of |x|α by a Newman-α rational operator. In this paper, we discuss the convergence rate of the operator Newman-α at the adjusted tangent nodes X={tan2kπ4n}nk=1, and finally obtain the exact approximation order O(1n2α). The result not only contains the approximation result in the case of α=1, but it is better than the conclusion when the node group is selected for the first and the second type of Chebyshev nodes, equidistant nodes etc.

Key words: rational approximation, Newman-α type rational operator, approximation order

CLC Number: