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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);
%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‘)
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