插值法实验报告.doc

1.(1).x=linspace(-5,5,11);y=1./(1+x.2);x0=linspace(-5,5,101);y0=1./(1+x.2);y1=interp1(x,y,x0,spline)y2=interp1(x,y,x0); A=ones(11,1) x (x.2) (x.3) (x.4) (x.5) (x.6) (x.7) (x.8) (x.9) (x.10)a=Ay;y3= a(1)+a(2).*x0+a(3).*x0.2+a(4).*x0.3+a(5).*x0.4+a(6).*x0.5+a(7).*x0.6+a(8).*x0.7+a(9).*x0.8+a(10).*x0.9+a(11).*x0.10; plot(x0,y3,r),gtext(Lagr.), hold on,plot(x0,y2,b),gtext(Pies.Lin.), hold on,plot(x0,y1,m),gtext(Spline)hold off(2).x=linspace(0,2*pi,11);y=cos(x);x0=linspace(0,pi,101);y0=cos(x0);y1=interp1(x,y,x0,spline)y2=interp1(x,y,x0); A=ones(11,1) x (x.2) (x.3) (x.4) (x.5) (x.6) (x.7) (x.8) (x.9) (x.10)a=Ay;y3= a(1)+a(2).*x0+a(3).*x0.2+a(4).*x0.3+a(5).*x0.4+a(6).*x0.5+a(7).*x0.6+a(8).*x0.7+a(9).*x0.8+a(10).*x0.9+a(11).*x0.10; plot(x0,y3,r),gtext(Lagr.), hold on,plot(x0,y2,b),gtext(Pies.Lin.), hold on,plot(x0,y1,m),gtext(Spline)hold off(3)x=linspace(0,pi,11);y=cos(x).10;x0=linspace(0,pi,101);y0=cos(x0).10;y1=interp1(x,y,x0,spline)y2=interp1(x,y,x0); A=ones(11,1) x (x.2) (x.3) (x.4) (x.5) (x.6) (x.7) (x.8) (x.9) (x.10)a=Ay;y3= a(1)+a(2).*x0+a(3).*x0.2+a(4).*x0.3+a(5).*x0.4+a(6).*x0.5+a(7).*x0.6+a(8).*x0.7+a(9).*x0.8+a(10).*x0.9+a(11).*x0.10; plot(x0,y3,r),gtext(Lagr.), hold on,plot(x0,y2,b),gtext(Pies.Lin.), hold on,plot(x0,y1,m),gtext(Spline)hold off2.(1).t=linspace(0,4,10);x=linspace(5,25,10);t,x=meshgrid(t,x);z=sin(t-1/200.*x)*2);t1,x1=meshgrid(linspace(0,4,100),linspace(5,25,100);z1=interp2(t,x,z,t1,x1,cubic);z2=interp2(t,x,z,t1,x1,nearest);z3=interp2(t,x,z,t1,x1,linear);mesh(t1,x1,z1);hold onmesh(t1,x1,z2);hold onmesh(t1,x1,z3);hold off三次插值，在这三种插值方法中效果最好最邻近插值，效果不是很好线性插值，效果一般(2) 取 e=1.5M文件：x=linspace(-1,1,10);y=linspace(-1,1,10);x,y=meshgrid(x,y);z=3/10+sin(16/15.*x-1.5)+(sin(16/15.*x-1.5).2+sin(16/15.*y-1.5)+(sin(16/15.*y-1.5).2x1,y1=meshgrid(linspace(-1,1,100),linspace(-1,1,100);z1=interp2(x,y,z,x1,y1,cubic);z2=interp2(x,y,z,x1,y1,nearest);z3=interp2(x,y,z,x1,y1,linear);mesh(x1,y1,z1);mesh(x1,y1,z2);mesh(x1,y1,z3);三次插值图形最临近插值线性插值3.x=linspace(0,8.534,13)y=0 0.914 5.060 7.772 8.717 9.083 9.144 9.083 8.992 8.687 7.376 2.073 0;x0=0:0.001:8.534;y1=interp1(x,y,x0);figure,plot(x,y,k*,x0,y1,-r)S=trapz(y1)*0.001S = 54.68944.执行M文件可知（1）所做功W(4)=8.15J (2)V（4）=4.0375.t=2:2:20;v=10 18 25 29 32 20 11 5 2 0;V=v/60;vi=interp1(t,V,ti); s=trapz(ti,vi)s = 4.90006. x=linspace(18,30,7);y=9.9617724 9.9543645 9.9468069 9.9390950 9.9312245 9.9231915 9.9149925;x1=18:30;y1=interp1(x,y,x1,spline)plot(x1,y1);gtext(y=9.9351799);从图像中可以看出在25号时金星与地球的距离的对数值为9.93517997. M文件：x=linspace(1,12,12);y=80.9 67.2 67.1 50.5 32.0 33.6 36.6 46.8 52.3 62.0 64.1 71.2;x1=linspace(1,12,120);y1=interp1(x,y,x1,spline);plot(x1,y1);从图像中可以看出，日照时间先是递增，随后逐渐增加，近似于二次抛物线8. y=0:400:2400;x=0:400:2800;z=1180 1320 1450 1420 1400 1300 700 9001230 1390 1500 1500 1400 900 1100 10601270 1500 1200 1100 1350 1450 1200 11501370 1500 1200 1100 1550 1600 1550 13801460 1500 1550 1600 1550 1600 1600 16001450 1480 1500 1550 1510 1430 1300 12001430 1450 1470 1320 1280 1200 1080 940; figure(1)meshz(x,y,z)title(源数据点)y0=0:25:2400;x0=0:25:2800;z0=interp2(x,y,z,x0,y0,linear);z1=interp2(x,y,z,x0,y0,nearest);z2=interp2(x,y,z,x0,y0,cubic);z3=interp2(x,y,z,x0,y0,spline);figure(2)surfc(x0,y0,z0)title(linear插值)figure(3)surfc(x0,y0,z1)title(nearest插值)figure(4)surfc(x0,y0,z2)title(cubic插值)figure(5