一、課題名稱Malab函數插值辦法二、目的和意義1、學會拉格朗日插值、牛頓插值、亨密特插值辦法，求函數的近似體現式，以解決其它實際問題；2、明確插值多項式和分段插值多項式各自的優缺點；3、熟悉插值辦法的程序編制；4、如果繪出插值函數的曲線，觀察其光滑性。三、計算公式拉格朗日插值的公式牛頓差值公式亨密特插值公式構造程序設計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;牛頓插值的程序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、成果討論和分析拉格朗日插值運行的成果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牛頓插值的運行成果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多項式插值的重要目的是用一種多項式擬合離散點上的