中山大学学报自然科学版 ›› 2016, Vol. 55 ›› Issue (6): 64-66.

• 研究论文 • 上一篇    下一篇

|x| 在Newman结点组的有理插值

张慧明1,李建俊2   

  1. 1. 河北地质大学数理学院,河北 石家庄 050031;
    2. 河北师范大学附属民族学院,河北 石家庄 050091
  • 收稿日期:2016-05-06 出版日期:2016-11-25 发布日期:2016-11-25
  • 通讯作者: 张慧明(1978年生),男;研究方向:函数逼近论;Email:zhanghm1978@126.com

On rational interpolation to |x| at the Newman nodes

ZHANG Huiming1, LI Jianjun2   

  1. 1. School of Mathematics & Physics, Hebei GEO University, Shijiazhuang 050031, China;
    2. Affiliated College of Minority Education, Hebei Normal University, Shijiazhuang 050091, China
  • Received:2016-05-06 Online:2016-11-25 Published:2016-11-25

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。

关键词: Newman结点, Newman型有理算子, Newman不等式, 有理插值, 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.

Key words: Newman nodes, Newman-type rational operators, Newman inequality, rational interpolation, order of approximation.

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