Multi-node higher order expansions of a function

被引：25

作者：

Han, XL ^{[1
]}

机构：

[1] Cent S Univ, Dept Appl Math & Appl Software, Changsha 410083, Peoples R China

来源：

JOURNAL OF APPROXIMATION THEORY | 2003年 / 124卷 / 02期

关键词：

numerical approximation; functional expansion; asymptotic error expansion; Bernstein polynomial; interpolation polynomial;

D O I：

10.1016/j.jat.2003.08.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By using the values and higher derivatives of a function at the given nodes, a kind of multinode higher order expansion of the function is, presented. The error terms of the expansions are given. Particular examples are the extensions of the Taylor polynomials, Bernstein polynomials and Lagrange interpolation polynomials. The expansions are numerical approximation polynomials and very useful particular for the functions for which the higher derivatives can be obtained easily. (C) 2003 Published by Elsevier Inc.

引用

页码：242 / 253

页数：12