最小二乘法原理及其matlab实现 程序.txt

最小二乘法原理及其MATLAB实现 线性拟合 多项式拟合 非线性拟合程序

线性拟合

x=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0];
y=[2.3201 2.6470 2.9070 3.2885 3.6008 3.9090 4.2147 4.5191 4.8232 5.1275];
p=polyfit(x,y,1)

p =

    3.1301    2.0141



多项式拟合

x=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0];
y=[2.3201 2.6470 2.9070 3.2885 3.6008 3.9090 4.2147 4.5191 4.8232 5.1275];
p=polyfit(x,y,2)

p =

   -0.1322    3.2755    1.9850



非线性拟合

x=[3.6 7.7 9.3 4.1 8.6 2.8 1.3 7.9 10.0 5.4];
y=[16.5 150.6 263.1 24.7 208.5 9.9 2.7 163.9 325 54.3];

a0=[0 0 0];
a=lsqcurvefit(@(a,x)a(1)*x.^2+a(2)*sin(x)+a(3)*x.^3,a0,x,y)
Optimization terminated: relative function value
 changing by less than OPTIONS.TolFun.

a =

    0.2269    0.3385    0.3022