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1、实验题目1 Lagrange插值摘要给定平面上n+1个不同的数据点：. - -：-=；-二：二二-=:则满足条件&仗Q 二k = O；ln的n次拉格朗日插值多项式臥和=y f&obco是存在唯一的。若二且匚J充分光滑，则当二士二时，有误差估计 式f叫）-%（叫）=寻等（X -SflXi-iJ. （x -xnX ? E ib前言利用拉格朗日插值多项式忌-求二的近似值程序设计流程L=0i=0否i=n?是输出y输入(xi,yi),ni=0,1,2,nx xxl=j *xlx xi jj=0,1，,i-1,i+1,nL=L+xl* y.ixl=1结束开始i=i+1拉格朗日插值框图问题 1 （1）N =
2、 5 时，程序运行如下：TestLag(inline(T./(1+x42), -5, 5, 5, 0.75:4.75);将区间-5,5分为了5段计算插值的点xi =0.75001.75002.75003.75004.7500计算出的插值yi =0.90540.52580.0096-0.3568-0.1595插值点处函数值yFact =0.64000.24620.11680.06640.0424计算误差err =-0.2654-0.27960.10720.42320.2020N = 10时，程序运行如下：TestLag(inline(1./(1+x.A2), -5, 5, 10, 0.75:4.
3、75);将区间-5,5分为了10段计算插值的点xi =0.75001.75002.75003.75004.7500计算出的插值yi =0.69070.23300.11220.1084-0.2360插值点处函数值 yFact =0.64000.24620.11680.06640.0424计算误差err =-0.05070.01320.0045-0.04200.2785N = 20时，程序运行如下：TestLag(inline(1./(1+x.A2), -5, 5, 20, 0.75:4.75);将区间-5,5分为了20段计算插值的点xi =0.75001.75002.75003.75004.75
4、00计算出的插值yi =0.64130.24910.12820.19036.4150插值点处函数值 yFact =0.64000.24620.11680.06640.0424计算误差err =-0.0013-0.0029-0.0114-0.1239-6.3726问题 1 （2）N = 5 时，程序运行如下：TestLag(inline(exp(x), -1, 1, 5, -0.95 -0.05 0.05 0.95); 将区间-1,1分为了5段 计算插值的点xi =-0.9500 -0.0500 0.0500 0.9500 计算出的插值yi =0.38630.95131.05122.5863插值
5、点处函数值yFact =0.38670.95121.05132.5857计算误差err =1.0e-003 *0.4471 -0.1051 0.1069 -0.6129N = 10 时，程序运行如下：TestLag(inline(exp(x), -1, 1, 10, -0.95 -0.05 0.05 0.95);将区间-1,1分为了10 段计算插值的点xi =-0.9500 -0.0500 0.0500 0.9500 计算出的插值yi =0.38670.95121.05132.5857插值点处函数值yFact =0.38670.95121.05132.5857计算误差err =1.0e-008
6、 *-0.3126 -0.0055 -0.0055 -0.3714N = 20 时，程序运行如下：TestLag(inline(exp(x), -1, 1, 20, -0.95 -0.05 0.05 0.95);将区间-1,1分为了20 段计算插值的点xi =-0.9500 -0.0500 0.0500 0.9500 计算出的插值yi =0.38670.95121.05132.5857插值点处函数值yFact =0.38670.95121.05132.5857计算误差err =1.0e-012 *0.73390 -0.0002 -0.5671问题 2 （1）N = 5 时，程序运行如下：Tes
7、tLag(inline(T./(1+x42), -1, 1, 5, -0.95 -0.05 0.05 0.95);将区间-1,1分为了5段计算插值的点xi =-0.9500-0.05000.05000.9500计算出的插值yi =0.51360.99780.99780.5136插值点处函数值yFact =0.52560.99750.99750.5256计算误差err =0.0121 -0.0002 -0.0002 0.0121N = 10时，程序运行如下：TestLag(inline(1./(1+x.A2), -1, 1, 10, -0.95 -0.05 0.05 0.95); 将区间-1,1
8、分为了10段计算插值的点xi =-0.9500-0.05000.05000.9500计算出的插值yi =0.52430.99750.99750.5243插值点处函数值 yFact =0.52560.99750.99750.5256计算误差err =0.00140.00000.00000.0014N = 20时，程序运行如下：TestLag(inline(T./(1+x42), -1, 1, 20, -0.95 -0.05 0.05 0.95); 将区间-1,1分为了20段计算插值的点xi =-0.9500-0.05000.05000.9500计算出的插值yi =0.52560.99750.99
9、750.5256插值点处函数值yFact =0.52560.99750.99750.5256计算误差err =1.0e-005 *-0.7023 0.0000 0.0000 -0.7023实验 2 （2）N = 5 时，程序运行如下：TestLag(inline(exp(x), -5, 5, 5, -4.75 -0.25 0.25 4.75); 将区间-5,5分为了5段计算插值的点xi =-4.7500 -0.25000.25004.7500计算出的插值yi =-1.9321 1.42750.5882123.7146插值点处函数值 yFact =0.00870.77881.2840115.58
10、43计算误差err =1.9408-0.64870.6958-8.1303N = 10 时，程序运行如下：TestLag(inline(exp(x), -5, 5, 10, -4.75 -0.25 0.25 4.75); 将区间-5,5分为了10 段计算插值的点xi =-4.7500 -0.25000.25004.7500计算出的插值yi =0.0425 0.77961.2848115.6630插值点处函数值 yFact =0.00870.7788 1.2840115.5843计算误差err =-0.0339-0.0008 -0.0008-0.0788N = 20 时，程序运行如下：TestL
11、ag(inline(exp(x), -5, 5, 20, -4.75 -0.25 0.25 4.75); 将区间-5,5分为了20 段计算插值的点xi =-4.7500 -0.25000.25004.7500计算出的插值yi =0.0087 0.77881.2840115.5843插值点处函数值 yFact =0.00870.77881.2840115.5843计算误差err =1.0e-007 *-0.09140.00000.0000-0.1434问题 3 （1）N =5 时，程序运行如下：TestLag2(inline(1./(1+x42), -1, 1, 5, -0.95 -0.05 0
12、.05 0.95); 将区间-1,1分为了5段计算插值的点xi =-0.9500-0.05000.05000.9500计算出的插值yi =0.52540.99780.99780.5254插值点处函数值yFact =0.52560.99750.99750.5256计算误差err =1.0e-003 *0.2071 -0.3011 -0.3011 0.2071N =10 时，程序运行如下：TestLag2(inline(1./(1+x.A2), -1, 1, 10, -0.95 -0.05 0.05 0.95); 将区间-1,1分为了10段计算插值的点xi =-0.9500-0.05000.050
13、00.9500计算出的插值yi =0.52550.99720.99720.5255插值点处函数值 yFact =0.52560.99750.99750.5256计算误差err =1.0e-003 *0.15620.26030.26030.1562N =20 时，程序运行如下：TestLag2(inline(1./(1+x42), -1, 1, 20, -0.95 -0.05 0.05 0.95); 将区间-1,1分为了20段计算插值的点xi=-0.9500-0.05000.05000.9500计算出的插值yi=0.52560.99750.99750.5256插值点处函数值yFact=0.52560.99750.99750.
