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## Re: Problem of polyfit

 From: Fredrik Lingvall Subject: Re: Problem of polyfit Date: Fri, 07 Oct 2005 14:41:17 +0200 User-agent: Mozilla Thunderbird 1.0.6 (X11/20051004)

```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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