插值實(shí)驗(yàn)實(shí)驗(yàn)報(bào)告

一、課題名稱Malab函數(shù)插值辦法二、目的和意義1、學(xué)會(huì)拉格朗日插值、牛頓插值、亨密特插值辦法，求函數(shù)的近似體現(xiàn)式，以解決其它實(shí)際問題；2、明確插值多項(xiàng)式和分段插值多項(xiàng)式各自的優(yōu)缺點(diǎn)；3、熟悉插值辦法的程序編制；4、如果繪出插值函數(shù)的曲線，觀察其光滑性。三、計(jì)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(gòu)造程序設(shè)計(jì)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(yùn)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(yùn)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(xiàng)式插值的重要目的是用一種多項(xiàng)式擬合離散點(diǎn)上的