Re: Problem of polyfit

[Paul Kienzle]

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.


- Paul



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