計算方法實驗三 不同曲線擬合比較

計算方法C2014-2015-2)學號：不同擬合曲線的比較】實驗報告學號：姓名：*****8課程教師：戴克儉教學班級：無10#i、方案1ii、方案2iii、方案3iv、方案4源程序清單如下：i、方案1圖1：求3次多項式?x=[194919501952195319551956195719581959196019611962196319651966196719681970197?y=[5.41675.51965.74285.87966.14656.28286.46536.59946.72096.62076.58596.72976.91727.2>>polyfit(k,y,3)圖2：求偏差ii、方案2圖3：求3次多項式format1ongk=[194919501952195319551956195719581959I9601961196219631965196619671968197019711972197419751976197719791980198219831984];SUJTlZl=5UJTL(Z(1j:；l);b=Z?；SUJTIZ2=5UJTL(b(lj:))；C=b?SUJTIZ3=5UJTL(C(lj:))；d二b?*b；5UJTiz4=SUJTl(d(lj:))；e=d?:+：x;sijjtiz5=sujtl(已(1』:));f=c?*c;sujtc<6=sujtl(f(lj:));A=[29sujtlkIsijjtlk2sujtlk3;sujtlk1sujtlk2sujtlkSsijjtlk-4;sujtlk2sujtlk3sujtlk4sujtix5;sujtlk3sujtlk4sujtlkSsujtlk6][5.41675.51965.74285.87966.14656.28286.46536.59946.72096.62076.58596.72976.91727.25387.45427.63687.85348.29928.52298.71779.08599.24209.37179.4974|9.75429.870510.154110.249510.3475];sujuy1=sujtl(y(1』:));i=x?：*:y;sujt^2=sujtl(i(1』:));j=b.忙匚sujt^3=sujtl(j(lj:));k=c?檸；sujt^4=sujtl(k〔1』:));Y=[sumylsumy2suiTLySsujrLy-l]?;B=irLv(：A：：i*Yiii、方案3圖4：求4次多項式formatlongk=[19491950195219531955195619571958195919601961196219631965196619671968197019711972197419751976197719791980198219831984];S1JJTLK1=SUJTl(Z(1j:));b=x.*x;sujtlk2=sujtl(bfl』:));c=b.*xsujtlk3=sujtl(c(1j:));d=b.*b;sujtlk4=sujtl(dfl』:));已二d.*z;sujtlk5=sujtl(efl』:));f=c.*c;sujtlk6=sujtl(f(lj:));g=c.*d;sujtlk7=sujtl(g(lj:));h=d.*d;sujtlk8=sujtl(h(1:));A=[29sujtlk1sujtlk2sujtlkSsujtlk4;sujtlk1sujtlk2sujtlkSsujtlk4sujtlkB;sujtlk2sujtlkSsujtlk4sujtlkBsujt^G;sujtlkSsujtlk4sujtlkBsujtlkGsujtlk7;sujtlk4sujtlkBsujtlkGsujtlkFsujtlkS^[5.41675.51965.74285.87966.14656.28286.46536.59946.72096.62076.58596.72976.91727.25387.45427.63687.85348.29928.52298.71779.08599.24209.37179.4974|9.75429.870510.154110.249510.3475];sujTLyl=sujTL(yfl』:));i=z.*y;sujTLy2=sujTL(i(lj:));j=b.*y;sujTLy3=sujTL(j(lj:));k=c.*y;sujTLy4=sujTL(k(lj:));l=d.*y;sujTLy5=sujTL(1(lj:));Y=[sujuylsujTLy2suinySsujTLy4sumy5]?;B=inv(A)*Yiv、方案4ttinclude<stdio.h>ttinclude<math.h>uoidmain(){doublex[29]={1949,1950,1952,1953,1955,1956,1957,1958,1959,1960,1961,19621963,1965,1966,1967,1968,1970,1971,1972,1974,1975,1976,1977[1979,1980,1982,1983,1984};doubley[29];inti;FILE*file;iF((File=Fopen("dtext.txt","w"))==NULL)return;For(i=B;i<29;i++){y[i]=sin(x[i]*B.3141592653);printFC'^.lfilFXn'^yti]);FprintF(File,"^.16lF",y[i]);Fclose(File);圖6：nafit函數(shù)M文件functionp=nafit(孟』y,m)A=zeros(m+ljm+1);fori=0:mforj=0:mA(i+ljj+l)=5uni(K."(i+j));endb(i+l)=suni(K."i.*y);enda=A\b?;p=fliplr(a?);圖7:命令行輸入?z=[0.30901710369959350.0000001150097536-0.5877851591522263-?y=[5.41675.51965.74285.87966.14656.28286.46536.59946.7209>>nafit(kjyf1)運算結(jié)果如下：⑴、方案1ans=1.0e+005*-0.000000000975200.00000576328328-0.011351604136567.45181855611415P(X)=745181.85611415-1135.160413656X+0.576328328XA2-0.000097520XTP(1969)=11.4973750142380600億P(2000)=14.3408021503128110億圖8擬合曲線：藍色線表示擬合曲線P(X)，紅色線表示真實數(shù)據(jù)誤差很大⑵、方案2B二1.0e+005*7.32370312500000-0.011156158447270.00000566389024-0.00000000095836P(X)=732370.3125-1115.615844727X+0.566389024XA2-0.000095836XTP(1969)=4.1277828774182126億P(2000)=6.7190460005076602億圖9擬合曲線：藍色線表示擬合曲線P(X)，紅色線表示真實數(shù)據(jù)誤差很大

⑶、方案3B=1.Oe+OO4*3.021250000000000.03209404296875-0.000053572368620.00000002799341-0.00000000000480P(X)=30212.5+320.9404296875X-0.5357236862XA2+0.0002799341XT-0.000000048XA4P(1969)=627.7665998683078200億P(2000)=671.4145749998278900億圖10擬合曲線：藍色線表示擬合曲線P(X),紅色線表示真實數(shù)據(jù)藍色線的數(shù)值全是上百億與實際嚴重不符誤差巨大

⑷、方案4ans=0.24147.7753P(X)=0.2414+7.7753sin(n*X/1O)P(1969)=2.6441006951177228億P(2000)=0.2413990828363674億圖11擬合曲線：藍色線表示擬合曲線P(X),整體看該曲線具有和sin近似的周期性質(zhì),與實際數(shù)據(jù)不是很符合。

結(jié)論如下：由上面的四種方案求出的擬合函數(shù)的圖像與實際數(shù)據(jù)曲線比較，或是從Q大小來看,會發(fā)現(xiàn)這4種方法或多或少都會出現(xiàn)相應的誤差。就誤差大小來看：方案一的結(jié)果普遍比實際數(shù)據(jù)高個1倍多，按常理來說，由matlab軟件封裝好的求多項式系數(shù)的函數(shù)polyfit的結(jié)果不應有錯，可是在本實驗中，預測人數(shù)和實際人數(shù)竟然會不符，可能是軟件安裝的有錯，此方