计算方法实验三 不同曲线拟合比较

计算方法C2014-2015-2)学号：不同拟合曲线的比较】实验报告学号：姓名：*****8课程教师：戴克俭教学班级：无10#i、方案1ii、方案2iii、方案3iv、方案4源程序清单如下：i、方案1图1：求3次多项式»x=[194919501952195319551956195719581959196019611962196319651966196719681970197»y=[5.41675.51965.74285.87966.14656.28286.46536.59946.72096.62076.58596.72976.91727.2>>polyfit(k,y,3)图2：求偏差ii、方案2图3：求3次多项式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・柠；sujt^4=sujtl(k〔1』:));Y=[sumylsumy2suiTLySsujrLy-l]?;B=irLv(：A：：i*Yiii、方案3图4：求4次多项式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);图6：nafit函数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?);图7:命令行输入»z=[0.30901710369959350.0000001150097536-0.5877851591522263-»y=[5.41675.51965.74285.87966.14656.28286.46536.59946.7209>>nafit(kjyf1)运算结果如下：⑴、方案1ans=1.0e+005*-0.000000000975200.00000576328328-0.011351604136567.45181855611415P(X)=745181.85611415-1135.160413656X+0.576328328XA2-0.000097520XTP(1969)=11.4973750142380600亿P(2000)=14.3408021503128110亿图8拟合曲线：蓝色线表示拟合曲线P(X)，红色线表示真实数据误差很大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)=4.1277828774182126亿P(2000)=6.7190460005076602亿图9拟合曲线：蓝色线表示拟合曲线P(X)，红色线表示真实数据误差很大

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)=627.7665998683078200亿P(2000)=671.4145749998278900亿图10拟合曲线：蓝色线表示拟合曲线P(X),红色线表示真实数据蓝色线的数值全是上百亿与实际严重不符误差巨大

⑷、方案4ans=0.24147.7753P(X)=0.2414+7.7753sin(n*X/1O)P(1969)=2.6441006951177228亿P(2000)=0.2413990828363674亿图11拟合曲线：蓝色线表示拟合曲线P(X),整体看该曲线具有和sin近似的周期性质,与实际数据不是很符合。

结论如下：由上面的四种方案求出的拟合函数的图像与实际数据曲线比较，或是从Q大小来看,会发现这4种方法或多或少都会出现相应的误差。就误差大小来看：方案一的结果普遍比实际数据高个1倍多，按常理来说，由matlab软件封装好的求多项式系数的函数polyfit的结果不应有错，可是在本实验中，预测人数和实际人数竟然会不符，可能是软件安装的有错，此方