最小二乘拟合

拟合函数

function C = lspoly(X,Y,M)

%This funciton implements the Least Squares Polynomial

%By abcat at 2014.5.7

%Input  -X is the 1*n abscissa vector

%       -Y is the 1*n ordinate vecotr

%       -M is the degree of the Least-Squares Polynomial

%Output -C is the coefficient list for the polynomial

n=length(X);

B=zeros(1:M+1);

F=zeros(n:M+1);

%File the columns of F with the powers of x

for k=1:M+1

    F(:,k)=X‘.^(k-1);

end

%Solve the linear system

A=F‘*F;

B=F‘*Y‘;

C=A\B

C=flipud(C);

主程序

%输入数据

x = [3.46   3.36   3.30   3.19   3.10   3.00   2.92  2.83   2.75   2.68];

y = [9.4141   9.0832   8.8945   8.5350   8.1286  7.7160   7.3556   6.9819   6.6267   6.2953];

%最小二乘拟合，参数分别是横、纵轴数据，拟合次数

c=lspoly(x,y,2);

y1=polyval(c,x);

%绘图

plot(x,y1)

hold on

plot(x,y,‘ro‘)

legend(‘Curve Fitting‘,‘Experimental Data‘)

grid on

xlabel(‘Abscissa Vector‘)

ylabel(‘Ordinate Vector‘)