Chebyshev多项式及其插值法在函数求导中的应用  

Application of Chebyshev Polynomial and Its Interpolation Method in Function Derivative

作　　者：周晶[1] 张红芹[1] 

机构地区：[1]吉林农业大学信息技术学院,长春130118

出　　处：《长春大学学报》2016年第12期56-58,68,共4页Journal of Changchun University

基　　金：吉林农业大学科研启动基金资助项目(2015043)

摘　　要：为了更精确地用插值函数的导数逼近复杂函数的导数,本文基于Chebyshev多项式和最小零偏差定理提出了一种应用Lagrange插值求复杂函数导数的新方法。我们首先以n+1次Chebyshev多项式的零点作为插值节点进行Lagrange插值,进而用插值函数的导数值逼近被插值函数的导数值。误差分析和数值算例表明本文所提出的方法在复杂函数求导中取得了良好的效果。In order to accurately make the approximation of interpolation function derivative to complex function derivative,this paper presents a new solution to complex function derivation by Lagrange interpolation based on Chebyshev polynomial and minimum zero deviation. We take the zero point of Chebyshev polynomial with n ＋ 1 degree as the interpolation node to make Lagrange interpolation,and then use the derivative value of interpolation function to approximate the derivative value of primitive function. The error analysis and numerical example show that the method presented in this paper achieves a better effect in complex function derivation.

关 键 词：CHEBYSHEV多项式 插值 最小零偏差 函数求导 

分 类 号：O241[理学—计算数学]