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《langrage和newton插值法的matlab实现》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。
1、仅供参考1．已知数据如下：0.20.40.60.81.00.980.920.810.640.38（1）用MATLAB语言编写按Langrage插值法和Newton插值法计算插值的程序，对以上数据进行插值；（2）利用MATLAB在第一个图中画出离散数据及插值函数曲线。(1.1)langrage插值法编程实现symsxx0=[0.2,0.4,0.6,0.8,1.0];y0=[0.98,0.92,0.81,0.64,0.38];fori=1:5a=1;forj=1:5ifj~=ia=expand(a*(x-x0(j)));endendb=1;fork=1:5ifk~=ib=b*(x0(i)-x0(
2、k));endendA(i)=expand(a/b);endL=0;forp=1:5L=L+y0(p)*A(p);endLL=-25/48*x^4+5/6*x^3-53/48*x^2+23/120*x+49/50（1.2）Newton插值程序实现clearallclcsymsxx0=[0.2,0.4,0.6,0.8,1.0];y0=[0.98,0.92,0.81,0.64,0.38];fork=1:5fori=1:ka=1;b=0;forj=1:kifj~=ia=a*(x0(i)-x0(j));endendb=b+y0(i)/a;endA(k)=b;endB=[1,(x-x0(1)),(x-
3、x0(1))*(x-x0(2)),(x-x0(1))*(x-x0(2))*(x-x0(3)),(x-x0(1))*(x-x0(2))*(x-x0(3))*(x-x0(4))];L1=A.*B;l=0;form=1:5l=l+L1(m);endL=expand(l)L=61/100+13/30*x+383/48*x^2-155/24*x^3+475/48*x^4（2）画图x0=[0.2,0.4,0.6,0.8,1.0];y0=[0.98,0.92,0.81,0.64,0.38];subplot(1,2,1);plot(x0(1),y0(1),'+r',x0(2),y0(2),'+r',x0(3
4、),y0(3),'+r',x0(4),y0(4),'+r',x0(5),y0(5),'+r')x=0:0.05:1;y=-25/48.*x.^4+5/6.*x.^3-53/48.*x.^2+23/120.*x+49/50;subplot(1,2,2);plot(x,y)2．给定函数，利用上题编好的Langrage插值程序（或Newton插值程序），分别取3个，5个、9个、11个等距节点作多项式插值，分别画出插值函数及原函数的图形，以验证Runge现象、分析插值多项式的收敛性。取三个节点如下clearclcx0=0:0.5:1;y0=1./(1+25.*x0.^2);symsxfori=1:3
5、a=1;forj=1:3ifj~=ia=expand(a*(x-x0(j)));endendb=1;fork=1:3ifk~=ib=b*(x0(i)-x0(k));endendA(i)=expand(a/b);endL=0;forp=1:3L=L+y0(p)*A(p);endLL=575/377*x^2-1875/754*x+1x1=0:0.0001:1;y1=1./(1+25.*x1.^2);y2=575/377.*x1.^2-1875/754.*x1+1;plot(x1,y1,'+r')holdonplot(x1,y2,'*k')取五个节点如下clearclcx0=0:0.25:1;y0
6、=1./(1+25.*x0.^2);symsxfori=1:5a=1;forj=1:5ifj~=ia=expand(a*(x-x0(j)));endendb=1;fork=1:5ifk~=ib=b*(x0(i)-x0(k));endendA(i)=expand(a/b);endL=0;forp=1:5L=L+y0(p)*A(p);endLL=1570000/3725137*x^4-9375000/3725137*x^3+16996575/3725137*x^2-25546875/7450274*x+1x1=0:0.0001:1;y1=1./(1+25.*x1.^2);y2=1570000/3
7、725137.*x1.^4-9375000/3725137.*x1.^3+16996575/3725137.*x1.^2-25546875/7450274.*x1+1;plot(x1,y1,'+r')holdonplot(x1,y2,'*k')取九个节点clearclcx0=0:0.125:1;y0=1./(1+25.*x0.^2);symsxfori=1:9a=1;forj=1:9ifj~=ia=expan
