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  1. function [c, flag]= approx(f,a,b,n,m)
  2. %create a vector for x data
  3. xdata=[];
  4. for j=0:m
  5.      xdata=[xdata,(a+(b-a)*j/m)];
  6. end
  7.  
  8. V=[];
  9. p=0;
  10. %create a Vandermore matrix by putting x data into the poewr of n
  11. for i=1:n+1
  12.  
  13.     V(:,i)=xdata.^(p);
  14.     p=p+1;
  15. end
  16. %find out y data
  17. ydata=feval(f,xdata);
  18. g=[ydata]';
  19. %conduct QR factorization
  20. [Q,R]=qr(V);
  21. %check whether the matrix is full rank and if not do not
  22. %compute c
  23. if ((rank(R) == size(R,1))||(rank(R) == size(R,2)))
  24.     c=[];
  25.     c=R(Q'*g);
  26.     flag=0;
  27. else
  28.     flag=1;
  29. end
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