數(shù)值分析作業(yè)1答案

1、當(dāng)時(shí)，求的二次插值多項(xiàng)式。1答案:2線性插值: 當(dāng)時(shí)二次插值:當(dāng)時(shí)3.h=466 715 950 1422 1635t=7.05 4.28 3.40 2.52 2.13hi=500 900 1500ti=interp1(h,t,hi,'nearest/linear/pchip/spline')最近插值:ti = 7.0500 3.4000 2.5200線性插值ti = 6.6718 3.5872 2.3772三次插值ti = 6.5533 3.5360 2.3765樣條插值ti = 6.4979 3.5224 2.38444x=1.55 1.62 1.63 1.70 1.92y

2、=2.587 2.415 2.465 3.031 3.341xi=1.57 1.68 1.81 1.90yi=interp1(x,y,xi,'linear/spline')線性插值: yi = 2.5379 2.8693 3.1860 3.3128樣條插值: yi =2.4162 2.8433 3.9093 3.6254x=1.55 1.62 1.63 1.70 1.92y=2.587 2.415 2.465 3.031 3.341x1=1.55:0.01:1.92y1= interp1(x,y,x1,'linear')y2=interp1(x,y,x1,

3、9;spline')plot(x,y,'*',x1,y1,':',x1,y2,'r')legend('樣本點(diǎn)','線性插值','三次樣條')5. x=-3 -2 0 3 4;y=18 10 2 2 5;p1=polyfit(x,y,1);poly2str(p1,'x')p2=polyfit(x,y,2);poly2str(p2,'x')p3=polyfit(x,y,3);poly2str(p3,'x') x1=-3:0.01:4;p11=pol

4、yval(p1,x1);p22=polyval(p2,x1);p33=polyval(p3,x1);plot(x,y,'ro',x1,p11,'b-',x1,p22,'g-',x1,p33,'k-','linewidth',2)legend('樣本點(diǎn)','一次擬合多項(xiàng)式','二次擬合多項(xiàng)式','三次擬合多項(xiàng)式')p1 =-1.6882 x + 8.0753p2 = 0.87283 x2 - 2.6455 x + 1.8247p3 =-0.038995

5、x3 + 0.91746 x2 - 2.263 x + 1.76926x=1 2 3 4 5 6;y=7.4 4.1 3.0 3.5 4.8 2.3x1=1:0.01:6;y1=interp1(x,y,x1,'linear');y2=interp1(x,y,x1,'spline');p1=polyfit(x,y,2);y3=polyval(p1,x1)p2=polyfit(x,y,4);y4=polyval(p2,x1);plot(x,y,'ro',x1,y1,'r-',x1,y2,'k-',x1,y3,'b-',x1,y4,'g-','linewidth',2)legend(&