function y = Chebyshev(y0,k,x0)
%切比雪夫多项式拟合
%written by Haidong Pan(OUC)
%输入参数介绍用k次切比雪夫多项式拟合输入数据（x0,y0)
%   Attention: (1) 输入的y0数组中可以有NaN (2)输入y0必须为列向量
L=length(y0);
gd=find(isfinite(y0(1:L)));
ngood=length(gd);
fprintf('   Points used: %d of %d\n',ngood,L)
T=zeros(L,k+1);
for i=1:L
    for j=1:k+1
        T(i,j)=cos((j-1)*acos(x0(i)));
    end
end
coef=regress(y0(gd),T(gd,:));
y=T*coef;

例子：

x0=0:1:270;y0=sind(x0);x0=x0';y0=y0';
plot(x0,y0,'k')
hold on
y=Chebyshev(y0,1,x0);plot(x0,y,'r')
y=Chebyshev(y0,2,x0);plot(x0,y,'g')
y=Chebyshev(y0,3,x0);plot(x0,y,'b')
y=Chebyshev(y0,4,x0);plot(x0,y,'m')
legend('Given','1阶','2阶','3阶','4阶')

http://s13/mw690/003cvAxDzy7cQecsl0E9c&690