Re: Problem of polyfit

[Fredrik Lingvall]

Paul Kienzle wrote:

> On Oct 6, 2005, at 5:46 AM, Tetsuro KURITA wrote:
>
> > The following code in "polyfit.m" never give the best fit data in the 
> > least squares sense as described in document.
> >
> >   X = (x * ones (1, n+1)) .^ (ones (l, 1) * (n : -1 : 0));
> >   p = X \ y;
> >
> > This code do nothing to mimimize `sumsq (p(x(i)) - y(i))'.
> >
> > I think this code should be modified as follows.
> >
> > X = (x * ones (1, n+1)) .^ (ones (l, 1) * (n: -1 : 0))
> > W = X'*X
> > z = X'*y
> > p = inv(W)*z
>
>
>  p = inv(X'*X)*X'*y
>    = inv(X)*inv(X')*X'*y
>    = inv(X)*I*y
>    = inv(X)*y
>    = X \ y
>
> wpolyfit does the same with weighting on y, except that it uses QR 
> decomposition to solve X \ y.
Try,

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

If you have singular values close to zero your in trouble.

Fredrik



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