实验一：三次样条插值（P56，例6）

一、实验目的：

1)　　掌握三次样条插值的运用

2)　　了解拉格朗日插值在高次上的误差

二、实验环境：Matlab6.5

三、实验内容：

　　1) 给定函数f(x)=1/(1+x2)，-5<=x<=5，节点xk=-5+k，(k=0,1,2…10)，用三次样条插值求S10(x)，S10’(-5)=f’(-5)，S10’(5)=f’(5)。

2）作原函数f(x)，拉格朗日插值函数Ln(x)，三次样条差值函数Sn(x)。画出三个函数的图像，比较它们的区别。

-Experiment I: cubic spline interpolation (P56, cases of 6) First, the experiment was: 1) cubic spline interpolation to master the use of 2) understanding of Lagrange interpolation in high-error second, experimental environment: Matlab6 .5 c, experimental elements: 1) a given function f (x) = 1/(1+ x2),-5 <= x <= 5, node xk =- 5+ k, (k = 0,1,2 ... 10), using cubic spline interpolation for S10 (x), S10 (-5) = f (-5), S10 (5) = f (5). 2) for the original function f (x), the Lagrange interpolation function Ln (x), cubic spline difference function Sn (x). Draw the three functions of images, compare the difference between them.