摘要
The condition of a polynomial interpolation operator and the numerical stabi-lity of an algorithm for polynomial interpolation are defined. The main result is that both Newton and Lagrange interpolation algorithms are numerically stable provided that the nodes are evenly distributed, but the extrapolation computation of these methods will lose the accuracy whatever the nodes are.
本文定义了多项式插值算子的条件数和多项式插值算法的数值稳定性等概念.主要研究结果是:若n和Y_max不太大,当结点等距分布时,Lagrange插值和Newton插值算法都是数值稳定的.但是不论结点如何分布,上述两法的外推计算可能是数值不稳定的.文中数值例子验证了这些理论结果.
基金
National Natural Science Foundation of China
