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一种Lagrange插值多项式的线性组合

付瑶, 王淑云, 孙毅   

  1. 吉林大学 数学学院, 长春 130012
  • 收稿日期:2006-01-20 修回日期:1900-01-01 出版日期:2007-01-26 发布日期:2007-01-26
  • 通讯作者: 王淑云

A Linear Combination of Lagrange Interpolation Polynomial

FU Yao, WANG Shuyun, SUN Yi   

  1. College of Mathematics, Jilin University, Changchun 130012, China
  • Received:2006-01-20 Revised:1900-01-01 Online:2007-01-26 Published:2007-01-26
  • Contact: WANG Shuyun

摘要: 以多项式的零点作为插值节点, 采用线性组合的方法构造了一个组合型的多项式算子Wn,r(f,x), 如果f(x)∈ Cj[-1,1](0≤j≤r, r为任意奇自然数), 则Wn,r(f,x)对f(x)的逼近程度达到最佳.

关键词: Lagrange插值多项式, 点态逼近阶, 线性组合, 算子

Abstract: Here we work out a combinational operator Wn,r(f,x) with zeros of the polynomial through the method of combination average. Convergence order of the operator Wn,r(f,x) is the best if Cj[-1,1](0≤j≤r, r, where r is an arbitrary odd natural number).

Key words: Lagrange interpolation polynomial, pointwise approximation order, linear combination, operator

中图分类号: 

  • O174.41