腐蝕電化學(xué)極化曲線(xiàn)擬合程序

22曲線(xiàn)擬合及其MATLAB程序?qū)嶒?yàn)任務(wù)：用最小二乘法將一組離散數(shù)據(jù)進(jìn)行曲線(xiàn)擬合，并用MATLAB做出曲線(xiàn)。實(shí)驗(yàn)要求：第三次作業(yè)的最后一題求函數(shù)關(guān)系并作出曲線(xiàn)，此組x和y的實(shí)驗(yàn)數(shù)據(jù)如下表所示。xi12345678910yi6.003.502.672.752.001.801.701.631.561.50實(shí)驗(yàn)內(nèi)容:在在MATLAB工作窗口輸入程序>>x=[12345678910];y=[6.003.502.672.752.001.801.701.631.561.50];plot(x,y,'r*'),legend('實(shí)驗(yàn)數(shù)據(jù)(xi,yi)')xlabel('x'),ylabel('y').title('實(shí)驗(yàn)數(shù)據(jù)點(diǎn)(xi,yi)的散點(diǎn)圖')運(yùn)行后屏幕顯示數(shù)據(jù)的散點(diǎn)圖(略)。6-實(shí)驗(yàn)數(shù)據(jù)點(diǎn)網(wǎng)汕的散點(diǎn)團(tuán)6-實(shí)驗(yàn)數(shù)據(jù)點(diǎn)網(wǎng)汕的散點(diǎn)團(tuán)5.5*實(shí)驗(yàn)數(shù)iSfxi.yi)4.54A3.52.5*-TOC\o"1-5"\h\z**卡IIIIIIT*：?2345678910編寫(xiě)下列MATLAB程序計(jì)算f(x)在(x,)處的函數(shù)值，即輸入程序>>symsa1a2a3a4;x=[12345678910];fi=al.*x43+a2.*x.A2+a3.*x+a4運(yùn)行后屏幕顯示關(guān)于al,a2,a3和a4的線(xiàn)性方程組fi=[a1+a2+a3+a4,8*a1+4*a2+2*a3+a4,27*a1+9*a2+3*a3+a4,64*a1+16*a2+4*a3+a4,125*a1+25*a2+5*a3+a4,216*a1+36*a2+6*a3+a4,343*a1+49*a2+7*a3+a4,512*a1+64*a2+8*a3+a4,729*a1+81*a2+9*a3+a4,1000*a1+100*a2+10*a3+a4]編寫(xiě)構(gòu)造誤差平方和的MATLAB程序>>y=[6.003.502.672.752.001.801.701.631.561.50];fi=[a1+a2+a3+a4,8*a1+4*a2+2*a3+a4,27*a1+9*a2+3*a3+a4,64*a1+16*a2+4*a3+a4,125*a1+25*a2+5*a3+a4,216*a1+36*a2+6*a3+a4,343*a1+49*a2+7*a3+a4,512*a1+64*a2+8*a3+a4,729*a1+81*a2+9*a3+a4,1000*a1+100*a2+10*a3+a4];fy=fi-y;fy2=fy.A2;J=sum(fy.A2)運(yùn)行后屏幕顯示誤差平方和如下J=(a1+a2+a3+a4-6)A2+(8*a1+4*a2+2*a3+a4-7/2)A2+(27*a1+9*a2+3*a3+a4-267/100)A2+(64*a1+16*a2+4*a3+a4-11/4)A2+(125*a1+25*a2+5*a3+a4-2)A2+(216*a1+36*a2+6*a3+a4-9/5)A2+(343*a1+49*a2+7*a3+a4-17/10)A2+(512*a1+64*a2+8*a3+a4-163/100)A2+(729*a1+81*a2+9*a3+a4-39/25)A2+(1000*a1+100*a2+10*a3+a4-3/2)A2J=0為求《，役，行3使J達(dá)到最小，只需利用極值的必要條件叫。(k二1,2,3,4)，得到關(guān)于a1,a2,S'a4的線(xiàn)性方程組，這可以由下面的MATLAB程序完成，即輸入程序>>symsa1a2a3a4J=(a1+a2+a3+a4-6)A2+(8*a1+4*a2+2*a3+a4-7/2)A2+(27*a1+9*a2+3*a3+a4-267/100)人2+(64*al+16*a2+4*a3+a4-ll/4)人2+(125*al+25*a2+5*a3+a4-2)人2+(216*al+36*a2+6*a3+a4-9/5)人2+(343*al+49*a2+7*a3+a4-l7/10)A2+(512*a1+64*a2+8*a3+a4-163/100)A2+(729*a1+81*a2+9*a3+a4-39/25)A2+(1000*a1+100*a2+10*a3+a4-3/2)A2;Ja1=diff(J,a1);Ja2=diff(J,a2);Ja3=diff(J,a3);Ja4=diff(J,a4);Ja11=simple(Ja1),Ja21=simple(Ja2),Ja31=simple(Ja3),Ja41=simple(Ja4),運(yùn)行后屏幕顯示J分別對(duì)al,a2,a3,a4的偏導(dǎo)數(shù)如下Jall=6050*a4+3956810*a1+441650*a2+50666*a3-497579/50Ja21=770*a4+441650*a1+50666*a2+6050*a3-66681/50Ja31=110*a4+50666*a1+6050*a2+770*a3-10679/50Ja41=20*a4+6050*a1+770*a2+110*a3-2511/50解線(xiàn)性方程組Ja11=0,Ja21=0,Ja31=0,Ja41=0,輸入下列程序>>A=[3956810,441650,50666,6050;441650,50666,6050,770;50666,6050,770,110;6050,770,110,20];B=[497579/50,66681/50,10679/50,2511/50];C=B/A,f=poly2sym(C)運(yùn)行后屏幕顯示擬合函數(shù)f及其系數(shù)C如下C=-0.01760.3744-2.64527.9627f=-5066427105276917/288230376151711744*xA3+6744376644764349/18014398509481984*xA2-2978180218619021/1125899906842624*x+1120645707277323/140737488355328故所求的擬合曲線(xiàn)為f(x)=-0.0176x3+0.3744x2-2.6452x+7.9627.編寫(xiě)下面的MATLAB程序估計(jì)其誤差，并作出擬合曲線(xiàn)和數(shù)據(jù)的圖形，輸入程序>>xi=[12345678910];y=[6.003.502.672.752.001.801.701.631.561.50];n=length(xi);f=-0.0176.*xi.A3+0.3744.*xi.A2-2.6452.*xi+7.9627;x=1:1:10;F=-0.0176.*xi43+0.3744.*xi42-2.6452.*xi+7.9627;fy=abs(f-y);fy2=fy.A2;Ew=max(fy),E1=sum(fy)/n,E2=sqrt((sum(fy2))/n)plot(xi,y,'r*'),holdon,plot(x,F,'b-'),holdofflegend('數(shù)據(jù)點(diǎn)(xi,yi)','擬合曲線(xiàn)y=f(x)'),xlabel('x'),ylabel('y'),tit