A survey on lagrange interpolation based on equally spaced nodes

被引：0

作者：

Revers, M ^{[1
]}

机构：

[1] Salzburg Univ, Dept Math, A-5020 Salzburg, Austria

来源：

ADVANCED PROBLEMS IN CONSTRUCTIVE APPROXIMATION | 2003年 / 142卷

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Lagrange interpolation polynomials based on the equidistant node system have not been a popular subject in approximation theory. This is due to some famous examples published by C. Runge in 1901 and later by S.N. Bernstein in 1918 which discouraged mathematicians from considering this method of interpolation. This paper provides a brief survey of Lagrange interpolation polynomials which are based on equidistant nodes including recent results on pointwise divergence properties and certain limit relations.

引用

页码：153 / 163

页数：11

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[21] Convergence of lagrange interpolation processes based on new systems of nodes [J].

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