Re: Problem of polyfit

[Fredrik Lingvall]

Tetsuro KURITA wrote:

> On 2005/10/07, at 17:32, Fredrik Lingvall wrote:
>
> > Can you post the output of  norm( inv(X'*X)*X'*y - (X'*X)\X'*y )?
>
>
> The result is as follows.
>
> octave> norm(inv(X'*X)*(X'*y) - (X'*X)\(X'*y))
> warning: matrix singular to machine precision, rcond = 3.02246e-112
> warning: attempting to find minimum norm solution
> ans = 50.504
>
> When calculating (X'*X)\(X'*y), warning message raise.
>
>
> =======================================================
>  Tetsuro KURITA
>   E-mail: address@hidden
> =======================================================
OK. Then X'*X do not have full rank (i.e., som eigenvalues are very 
small) and the inverse do not exist.

Try for example,

[U,D,V] = svd(X'*X);
semilogy(diag(D));

You will probably see that some singular values are very close to zero 
and a direct inverse of
X'*X will result in strong noise amplification.

Fredrik





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