DERIVATIVE ERROR APPROXIMATION  FOR LAGRANGE INTERPOLATION

薛亚奎; 吴文利

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DERIVATIVE ERROR APPROXIMATION FOR LAGRANGE INTERPOLATION

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- DERIVATIVE ERROR APPROXIMATION FOR LAGRANGE INTERPOLATION
- 关于Lagrange插值导数的误差估计
- Issue 4, (1996)
- 作者机构：
  
  1. 华北工学院
  2. 太原经济管理干部学院
- 作者简介：
- 基金信息：
- DOI：
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- Published：1996
- 稿件说明：
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薛亚奎, 吴文利. DERIVATIVE ERROR APPROXIMATION FOR LAGRANGE INTERPOLATION[J]. 1996, (4).
DOI：

薛亚奎, 吴文利. DERIVATIVE ERROR APPROXIMATION FOR LAGRANGE INTERPOLATION[J]. 1996, (4). DOI：

摘要

关于Ｌａｇｒａｎｇｅ插值导数的误差估计曾提出过以下猜想：对任意ｎ＋１次连续可微的函数ｆ和任意ｎ＋１个连续点，ｎ次ｌａｇｒａｎｇｅ插值多项式Ｌ满足：‖ｆ（ｊ）－Ｌ（ｊ）‖≤‖ｗ（ｊ）‖‖ｆ（ｎ＋１）‖（ｎ＋１）！，其中ｊ是所有的整数，‖·‖表示上确界范数．ＧａｒｙＷＨｏｗｅｌ在文献［１］中证明了ｊ＝ｎ时猜想成立，ｊ＝１，２，…，ｎ－１猜想没被解决，而仅得到了‖ｆ（ｊ）－Ｌ（ｊ）‖≤‖ｗ（ｊ）‖‖ｆ（ｎ＋１）‖ｊ！（ｎ＋１－ｊ）！这样的估计式，本文主要研究ｊ＝ｎ－１时，可以得到了较好的估计式

Abstract

In 《An Extension of Cauchy′s Bound for the Error of Lagrange Interpolation》

Gary W Howell gave that for any n+1 times continuously differentiable funtion f and any choice of n+1 knots

the lagrange interpolation polynomial L of degree n satisfies: ‖ f (j) -L (j) ‖≤‖w (j) ‖‖f (n+1) ‖(n+1)!

it is also shown that for j=1

…

n-1

‖f (j) -L (j) ‖≤‖w (j) ‖‖f (n+1) ‖j!(n+1-j)!

where j is integer and ‖·‖ denotes the supremum norm

when j=n-1 . We′ll get a better approximation formula.

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