曲线拟合的最小二乘法1、%采用二次多项式拟合%a的输出为多项式各项系数%b为拟合曲线各点函数值%phi为输出的曲线拟合函数x=0:5:55;y=[01.272.162.863.443.874.154.374.514.584.024.64];a=polyfit(x,y,2)b=polyval(a,x)symstphi=a(1)*t^2+a(2)*t+a(3)运行结果：>>leastwaya=-0.00240.20370.2305b=Columns1through50.23051.18942.02932.75023.3521Columns6through103.83494.19874.44354.56934.5760Columns11through124.46374.2324phi=2-0.00238051948051948162t+0.203690809190809258t+0.2304670329670317492、%采用三次多项式拟合x=0:5:55;y=[01.272.162.863.443.874.154.374.514.584.024.64];a=polyfit(x,y,3)b=polyval(a,x)symstphi=a(1)*t^3+a(2)*t^2+a(3)*t+a(4)运行结果：>>leastwaya=0.0000-0.00520.26340.0178b=Columns1through50.01781.20872.16462.91133.4745Columns6through103.88004.15364.32114.40824.4407Columns11through124.44444.4450phi=320.0000343641543641541613t-0.00521556221556219567t+0.263398527398526872t+0.01783882783883230383、%delta为拟合函数值与原函数值的误差clcclearx=0:5:55;y=[01.272.162.863.443.874.154.374.514.584.024.64];a=polyfit(x,y,3);b=polyval(a,x);forj=1:12delta=b(j)-y(j)endsymstphi=a(1)*t^3+a(2)*t^2+a(3)*t+a(4)运行结果：delta=0.0178delta=-0.0613delta=0.0046delta=0.0513delta=0.0345delta=0.0100delta=0.0036delta=-0.0489delta=-0.1018delta=-0.1393delta=0.4244delta=-0.1950phi=320.0000343641543641541613t-0.00521556221556219567t+0.263398527398526872t+0.01783882783883230384、%采用四次多项式拟合与三次多项式拟合进行比较%输出其与原函数值的误差再与之前输出的三次与原函误差进行比较%delta4为四次与原函的误差clcclearx=0:5:55;y=[01.272.162.863.443.874.154.374.514.584.024.64];a=polyfit(x,y,4);b=polyval(a,x)forj=1:12delta4=b(j)-y(j)endsymstphi=a(1)*t^4+a(2)*t^3+a(3)*t^2+a(4)*t+a(5)运行结果：b=Columns1through50.06041.17392.12202.89453.4900Columns6through103.91624.18984.33664.39144.3981Columns11through124.40954.4876delta4=0.0604delta4=-0.0961delta4=-0.0380delta4=0.0345delta4=0.0500delta4=0.0462delta4=0.0398delta4=-0.0334delta4=-0.1186delta4=-0.1819delta4=0.3895delta4=-0.1524phi=-6430.60256410256410728810t-0.0000319178969178975504t2-0.00293227466977464190t+0.238069314944314520t+0.06044871794871947705、%分别采用二次、四次、六次、九次多项式拟合并画出其曲线进行比较clcclearx=0:5:55;y=[01.272.162.863.443.874.154.374.514.584.024.64];a2=polyfit(x,y,2);b2=polyval(a2,x);a4=polyfit(x,y,4);b4=polyval(a4,x);a6=polyfit(x,y,6);b6=polyval(a6,x);a9=polyfit(x,y,9);b9=polyval(a9,x);plot(x,b2,'r-^');holdonplot(x,b4,'g->');holdonplot(x,b6,'b-*');holdonplot(x,b9,'y-+');holdonplot(x,y,'ko');title('含碳量-时间曲线');xlabel('时间t（分）');ylabel('含碳量y（10^-^4）');legend('二次拟合曲线','四次拟合曲线','六次拟合曲线','九次拟合曲线','原函数点',);运行结果：警告:多项式未正确设置条件。请添加具有不同X值的点，减少多项式的阶数，或者尝试按照HELPPOLYFIT中所述进行居中和缩放。>Inpolyfitat75Inleastwayat9警告:多项式未正确设置条件。请添加具有不同X值的点，减少多项式的阶数，或者尝试按照HELPPOLYFIT中所述进行居中和缩放。>Inpolyfitat75Inleastwayat11局部放大图
