最小二乘逼近

實(shí)驗(yàn)名稱實(shí)驗(yàn)?zāi)康暮鸵?/p>

最小二乘逼近握最小二乘逼近的的基本思路和步驟養(yǎng)使用軟編程及上機(jī)調(diào)試能力實(shí)驗(yàn)內(nèi)容和步驟：實(shí)驗(yàn)內(nèi)：用最小逼近法計(jì)算以下3題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試驗(yàn)步：1）實(shí)驗(yàn)編程2）運(yùn)行結(jié)果實(shí)驗(yàn)過(guò)1GiventhetableXiYi

-0.1

0.1

0.4

0.9

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

>>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('據(jù)點(diǎn)(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('數(shù)據(jù)點(diǎn)(xi,yi)','合曲線y=f(x)');xlabel('x');ylabel('y');title('據(jù)點(diǎn)(和合曲線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('數(shù)據(jù)點(diǎn)(xi,yi)','合曲線y=f(x)');xlabel('x');ylabel('y');title('據(jù)點(diǎn)(和合曲線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('數(shù)據(jù)點(diǎn)(xi,yi)','合曲線y=f(x)');xlabel('x');ylabel('y');title('據(jù)點(diǎn)(和合曲線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('據(jù)點(diǎn)(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('數(shù)據(jù)點(diǎn)(xi,yi)','合曲線y=f(x)')t