关于Michalik连分式插值的多点扩展应用

An extended algorithm for Michalik's continued fraction interpolation

本文给出一种关于Michalik的连分式插值的扩展算法。它使给出的连分式插值更加准确,结果更加精确。该方法在Michalik连分式原节点数的基础上再多加一个新的函数节点,并利用三项递推公式计算出该节点的函数值,然后添加不同的插值节点进行误差比较,寻找出最优的插值节点。该方法能使给出的连分式插值更加准确。本文利用构造出的新的插值节点及其原有的函数节点可以计算出一个新的连分式插值函数,从而能够很好地逼近原函数。

An extended algorithm for Michalik's continuous fractional interpolation is given by a given complex function,which makes the given fractional interpolation more accurate.The method is to calculate the function value of the node by adding more function nodes based on the number of original nodes of Michalik,so that the given interpolation node can be more accurate,and the new interpolation node and the original function node are utilized.Construct a new continuous fractional interpolation function,which can be close to the original function.