On rational interpolation to |x| at the Newman nodes

ZHANG Huiming; LI Jianjun

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On rational interpolation to |x| at the Newman nodes

更新时间：2023-12-11

- On rational interpolation to |x| at the Newman nodes
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 55, Issue 6, Pages: 64-66(2016)
- 作者机构：
  
  1. 河北地质大学数理学院,河北,石家庄,050031
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2016，
  
  Published Online：25 November 2016，
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ZHANG Huiming, LI Jianjun. On rational interpolation to |x| at the Newman nodes. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 55(6):64-66(2016)
DOI：

ZHANG Huiming, LI Jianjun. On rational interpolation to |x| at the Newman nodes. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 55(6):64-66(2016) DOI：

摘要

研究Newman型有理算子逼近 |x| 的收敛速度，在Newman结点组的零点附近［0

e－〖KF(〗n〖KF)〗］增加结点。通过对Newman不等式进行改进，得到确切的逼近阶为O〖JB((〗〖SX(〗1〖〗〖KF(〗n〖KF)〗e〖SX(〗3〖KF(〗n〖KF)〗〖〗2〖SX)〗〖SX)〗〖JB))〗

这个结果优于Newman的经典结果。进一步说明：在零点附近增加结点可以提高原来的逼近阶。

Abstract

The rate of convergence for Newmantype rational interpolation to |x| is studied

and nodes near the zero of the Newman nodes are increased. Through the improvement of Newmans inequality

it is proved that the exact order of approximation is O〖JB((〗〖SX(〗1〖〗〖KF(〗n〖KF)〗e〖SX(〗3〖KF(〗n〖KF)〗〖〗2〖SX)〗〖SX)〗〖JB))〗

 the result is better than the classical results of Newman. Further explanation: increases nodes in the near zero can improve the approximation order of the original.

关键词

Newman结点Newman型有理算子Newman不等式有理插值逼近阶

Keywords

Newman nodesNewman-type rational operatorsNewman inequalityrational interpolationorder of approximation.

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