插值实验实验报告

一、课题名称Malab函数插值办法二、目的和意义1、学会拉格朗日插值、牛顿插值、亨密特插值办法，求函数的近似体现式，以解决其它实际问题；2、明确插值多项式和分段插值多项式各自的优缺点；3、熟悉插值办法的程序编制；4、如果绘出插值函数的曲线，观察其光滑性。三、计算公式拉格朗日插值的公式牛顿差值公式亨密特插值公式构造程序设计拉格朗日插值的程序function[c,l]=lagan1(x,y)x=input('x=:');y=input('y=:');w=length(x);n=w-1;l=zeros(w,w);fork=1:n+1v=1;forj=1:n+1ifk~=jv=conv(v,poly(x(j)))/(x(k)-x(j));endendl(k,:)=vEndc=y*l;牛顿插值的程序function[c,l]=lagan(x,y)x=input('x=:');y=input('y=:');n=length(x);d=zeros(n,n);d(:,1)=y';forj=2:nfork=j:nd(k,j)=(d(k,j-1)-d(k-1,j-1))/(x(k)-x(k-j+1));endendc=d(n,n);fork=(n-1):-1:1c=conv(c,poly(x(k)));m=length(c);c(m)=c(m)+d(k,k);end六、成果讨论和分析拉格朗日插值运行的成果x=:[0.40.550.650.800.951.05]y=:[0.410750.578150.696750.91.001.25382]l=1.0e+003*-0.18650.7459-1.17760.9167-0.35170.0532000000000000000000000000000000l=1.0e+003*-0.18650.7459-1.17760.9167-0.35170.05321.3333-5.13337.7300-5.67122.0177-0.2766000000000000000000000000l=1.0e+004*-0.01860.0746-0.11780.0917-0.03520.00530.1333-0.51330.7730-0.56710.-0.0277-0.22220.8333-1.21720.8626-0.29550.0390000000000000000000l=1.0e+004*-0.01860.0746-0.11780.0917-0.03520.00530.1333-0.51330.7730-0.56710.-0.0277-0.22220.8333-1.21720.8626-0.29550.03900.1778-0.64000.8951-0.60690.1994-0.0254000000000000l=1.0e+004*-0.01860.0746-0.11780.0917-0.03520.00530.1333-0.51330.7730-0.56710.-0.0277-0.22220.8333-1.21720.8626-0.29550.03900.1778-0.64000.8951-0.60690.1994-0.0254-0.10100.3485-0.46840.3067-0.09780.0121000000l=1.0e+004*-0.01860.0746-0.11780.0917-0.03520.00530.1333-0.51330.7730-0.56710.-0.0277-0.22220.8333-1.21720.8626-0.29550.03900.1778-0.64000.8951-0.60690.1994-0.0254-0.10100.3485-0.46840.3067-0.09780.01210.0308-0.10310.1353-0.08690.0273-0.0033ans=121.6264-422.7503572.5667-377.2549121.9718-15.0845121.6264*0.596^5+(-422.7503)*0.596^4+572.5667*0.596^3+(-377.2549)*0.596^2+121.9718*0.596-15.0845ans=0.6257121.6264*0.99^5+(-422.7503)*0.99^4+572.5667*0.99^3+(-377.2549)*0.99^2+121.9718*0.99-15.0845ans=1.0542牛顿插值的运行成果x=:[0.4,0.55,0.65,0.80,0.95,1.05]y=:[0.41075,0.57815,0.69675,0.90,1.00,1.25382]ans=121.6264-422.7503572.5667-377.2549121.9718-15.0845121.6264*0.596^5+(-422.7503)*0.596^4+572.5667*0.596^3+(-377.2549)*0.596^2+121.9718*0.596-15.0845ans=0.6257121.6264*0.99^5+(-422.7503)*0.99^4+572.5667*0.99^3+(-377.2549)*0.99^2+121.9718*0.99-15.0845ans=1.0542多项式插值的重要目的是用一种多项式拟合离散点上的