特殊节点的Lagrange多项式对光滑函数的逼近阶

THE APPROXIMATE ORDER OF LAGRANGE POLNORMIAL TO THE SMOOTH FUNCTION WITH SPECIAL NODE

本文讨论以Ｃｈｅｂｙｓｈｅｖ多项式的零点为节点的Ｌａｇｒａｎｇｅ型多项式来逼近光滑函数的逼近阶。

This paper discusses the approximating order of lagrange polynormial to the smooth function with the node being the null of the chebyshev polynormial It improves the oretically the approximate order from O(n -12 ) to O(n -1 ) and to 0(n -2 ),and gives the exact erplaination of 0(n -1 ).