最小二乘逼近

实验名称实验目的和要求

最小二乘逼近握最小二乘逼近的的基本思路和步骤养使用软编程及上机调试能力实验内容和步骤：实验内：用最小逼近法计算以下3题1tableXiYi

-0.1

0.1

0.4

0.9

1.6aquadraticandwiththe2Findtheleastofdegree1,2andforinthefollowingComputeerrorincasedataandpolynomials.XiYi

1.0

1.1

1.3

1.5

1.9

2.13Xi

4.2

4.54.7

5.1

5.5

6.3

6.8Yi

113.18142.05167.53195.14224.87256.73299.50326.72Constructthedegree1,2andcomputetheerrors.ofbe,computetheerrors试验步：1）实验编程2）运行结果实验过1GiventhetableXiYi

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0.1

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0.9

1.6Solvequadraticfittingthesquares解：>>x=[-202];y=[-0.10.4plot(x,y,'r*'),数点(

>>a=0.42000.4086>>a=0.08570.39170.40862thesquaresofthedatainthefollowingtable.Computeerrorincase.Graphthepolynomials.XiYi

1.0

1.1

1.3

1.5

1.9

2.1解：];y=[1.842.212.45plot(x,y,'r*'),legend('据点(xi,yi)')>>a=polyfit(x,y,1)a=>>a=-0.01091.2533

a=polyfit(x,y,3)a=-0.01000.03530.6290>>1.11.5y=[1.842.212.45x1=1.0:0.001:2.1;y1=1.2196.*x1+0.6209;y2=1.2196.*x+0.6209;plot(x,y,'r*',x1,y1,'b-');legend('数据点(xi,yi)','合曲线y=f(x)');xlabel('x');ylabel('y');title('据点(和合曲线y=f(x)的形'1.11.5y=[1.842.212.45y2=-0.0109.*x.^2+1.2533.*x+0.5966;plot(x,y,'r*',x1,y1,'b-');legend('数据点(xi,yi)','合曲线y=f(x)');xlabel('x');ylabel('y');title('据点(和合曲线y=f(x)的形'

1.11.5y=[1.842.212.45x1=1.0:0.001:2.1;y1=-0.0100.*x1.^3+0.0353.*x1.^2+1.1850.*x1+0.6290;y2=-0.0100.*x.^3+0.0353.*x.^2+1.1850.*x+0.6290;plot(x,y,'r*',x1,y1,'b-');legend('数据点(xi,yi)','合曲线y=f(x)');xlabel('x');ylabel('y');title('据点(和合曲线y=f(x)的形'3Giventhedata:Xi

Yi

113.18130.11195.14224.87256.73299.50326.72thesquaresof1,2andandcomputetheerrors.(2)Constructsquaresoftheformbe,computetheerrors解x=[4.06.3y=[102.56113.18167.53195.14224.87256.73299.50326.72];plot(x,y,'r*'),legend('据点(xi,yi)')ylabel('y'),a=polyfit(x,y,1)a=72.0845

>>a=polyfit(x,y,2)a=-1.14351.2356>>a=-0.01376.8456-2.37923.4291x=[4.06.3y=[102.56113.18167.53195.14224.87256.73299.50326.72];Y=log(y);b=B,a=exp(A)n=length(x);X=8:-0.01:1;Y=a*exp(b.*X);f=a*exp(b.*x);plot(x,y,'r*',X,Y,'b-'),legend('数据点(xi,yi)','合曲线y=f(x)')t