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1、插值：例1编写程序如下：clearx0=[0,3,5,7,9,11,12,13,14,15];y0=[0,1.2,1.7,2.0,2.1,2.0,1.8,1.2,1.0,1.6];x=13:0.1:15;y1=lagrange(x0,y0,x);y2=interp1(x0,y0,x);y3=interp1(x0,y0,x,'spline');pp1=csape(x0,y0);y4=ppval(pp1,x);pp2=csape(x0,y0,'not-a-knot');y5=ppval(pp2,x);fprintf('比较不同插值结果下的边界值的差别:')fprintf('x,y1,y2,y3
2、,y4,y5')xianshi=[x',y1',y2',y3',y4',y5'];fprintf('%ft%ft%ft%ft%ft%f',xianshi')subplot(2,2,1),plot(x0,y0,'*r',x,y1),title('lagrange')subplot(2,2,2),plot(x0,y0,'*b',x,y2),title('linear')subplot(2,2,3),plot(x0,y0,'*y',x,y3),title('spline')subplot(2,2,4),plot(x0,y0,'*g',x,y4),title('splinecsape
3、1')subplot(2,2,4),plot(x0,y0,'*c',x,y5),title('splinecsape2')dyx0=ppval(fnder(pp1),x0(1))%求x=0处的导数ytemp=y3(13:15);index=find(ytemp==min(ytemp));xymin=[x(13+index),ytemp(index)]functiony=lagrange(x0,y0,x);n=length(x0);m=length(x);fori=1:mz=x(i);s=0.0;fork=1:np=1.0;forj=1:nifj~=kp=p*(z-x0(j))/(x0(k)-x
4、0(j));endends=p*y0(k)+s;endy(i)=s;end比较不同插值结果下的边界值的差别:x,y1,y2y3,y4,y513.0000001.2000001.2000001.2000001.2000001.20000013.1000001.1398561.1800001.1500901.1506011.15009013.2000001.0848011.1600001.1062571.1073611.10625713.3000001.0363881.1400001.0687141.0704191.06871413.4000000.9961671.1200001.0376751.
5、0399161.03767513.5000000.9656441.1000001.0133551.0159941.01335513.6000000.9462201.0800000.9959660.9987910.99596613.7000000.9391291.0600000.9857220.9884500.98572213.8000000.9453611.0400000.9828380.9851110.98283813.9000000.9655751.0200000.9875260.9889140.98752614.0000001.0000001.0000001.0000001.000000
6、1.00000014.1000001.0483241.0600001.0204741.0185671.02047414.2000001.1095681.1200001.0491621.0450441.04916214.3000001.1819451.1800001.0862781.0799181.08627814.4000001.2627041.2400001.1320341.1236751.13203414.5000001.3479551.3000001.1866451.1768011.18664514.6000001.4324811.3600001.2503251.2397831.2503
7、2514.7000001.5095221.4200001.3232861.3131081.32328614.8000001.5705451.4800001.4057431.3972611.40574314.9000001.6049911.5400001.4979101.4927301.49791015.0000001.6000001.6000001.6000001.6000001.600000dy
