lsm_v01.m

最小二乘法(Least-square method)在matlab平台下的实现程序。

clear all,clc
x=0:1:10;
P=[0.5,-2,0,0];  %y=0.5*x.^3-3.5*x.^2-2.5*x-10;
y=polyval(P,x);
[temp,N]=size(x);   % N: elements number
[temp,highorder]=size(P);
highorder=highorder-1;    % the highest order of the polynomial
P0=zeros(1,highorder+1);    % A*P0=b
A=zeros(highorder+1,highorder+1);
b=zeros(highorder+1,1);
for row=1:(highorder+1)
    for colum=row:(highorder+1)
        for ii=1:N
            A(row,colum)=A(row,colum)+power(x(ii),colum-1)*power(x(ii),row-1);
        end
        A(colum,row)=A(row,colum);
    end
    for ii=1:N
        b(row)=b(row)+y(ii)*power(x(ii),row-1);
    end
end
P0=inv(A)*b;
Pfit=zeros(1,highorder+1);
Pfit=P0(highorder+1:-1:1)';
[P;Pfit]
yfit=polyval(Pfit,x);
plot(x,y,'b*',x,yfit,'r-')
grid on