一种基于多次拉格朗日插值的函数值确定方法

A confirmation method of function values based on several times Lagrange interpolation

快速确定一类以曲线图形形式出现的函数值,提出一种基于数值分析的计算方法.该算法以所给曲线上的点的函数值为基础,通过多次拉格朗日插值确定这类函数在任意点的函数值.实例计算显示,本文算法的平均相对误差为2.1%,所提算法易于通过编程在计算机上实现,且在计算精度和计算效率上均优于现有工程方法.

In order to confirm the function value more precisely and quickly from a kind of func‐tion that was provided in the form of curve graph ,an algorithm was put forward on numerical value method .Based on the provided function values of the points that are in the curve ,the al‐gorithm confirmed the function value of any point by several times Lagrange interpolation .fur‐ther more ,the algorithm is easily carried out by computer program .In order to compare the al‐gorithm put forward in this paper with the traditional one ,a certain practical example was cal‐culated by the two algorithm respectively .The result is that the average relative error of the al‐gorithm put forward in this paper is 2.1% .This indicates that the algorithm put forward in this paper is better than the existing engineering method .