数值分析实验作业matlab编程课题8.docxVIP

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=[0 1.27 2.16 2.86 3.44 3.87 4.15 4.37 4.51 4.58 4.02 4.64]; a=polyfit(x,y,2) b=polyval(a,x) syms t phi=a(1)*t^2+a(2)*t+a(3) 运行结果： leastway a = -0.0024 0.2037 0.2305 b = Columns 1 through 5 0.2305 1.1894 2.0293 2.7502 3.3521 Columns 6 through 10 3.8349 4.1987 4.4435 4.5693 4.5760 Columns 11 through 12 4.4637 4.2324 phi = 2 -0.00238051948051948162 t + 0.203690809190809258 t + 0.230467032967031749 2、 %采用三次多项式拟合 x=0:5:55; y=[0 1.27 2.16 2.86 3.44 3.87 4.15 4.37 4.51 4.58 4.02 4.64]; a=polyfit(x,y,3) b=polyval(a,x) syms t phi=a(1)*t^3+a(2)*t^2+a(3)*t+a(4) 运行结果： leastway a = 0.0000 -0.0052 0.2634 0.0178 b = Columns 1 through 5 0.0178 1.2087 2.1646 2.9113 3.4745 Columns 6 through 10 3.8800 4.1536 4.3211 4.4082 4.4407 Columns 11 through 12 4.4444 4.4450 phi = 3 2 0.0000343641543641541613 t - 0.00521556221556219567 t + 0.263398527398526872 t + 0.0178388278388323038 3、 %delta为拟合函数值与原函数值的误差 clc clear x=0:5:55; y=[0 1.27 2.16 2.86 3.44 3.87 4.15 4.37 4.51 4.58 4.02 4.64]; a=polyfit(x,y,3); b=polyval(a,x); for j=1:12 delta=b(j)-y(j) end syms t phi=a(1)*t^3+a(2)*t^2+a(3)*t+a(4) 运行结果： delta = 0.0178 delta = -0.0613 delta = 0.0046 delta = 0.0513 delta = 0.0345 delta = 0.0100 delta = 0.0036 delta = -0.0489 delta = -0.1018 delta = -0.1393 delta = 0.4244 delta = -0.1950 phi = 3 2 0.0000343641543641541613 t - 0.00521556221556219567 t + 0.263398527398526872 t + 0.0178388278388323038 4、 %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 clc clear x=0:5:55; y=[0 1.27 2.16 2.86 3.44 3.87 4.15 4.37 4.51 4.58 4.02 4.64]; a=polyfit(x,y,4); b=polyval(a,x) for j=1:12