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## Re: Problem of polyfit

**From**: |
Paul Kienzle |

**Subject**: |
Re: Problem of polyfit |

**Date**: |
Thu, 6 Oct 2005 21:45:45 -0400 |

On Oct 6, 2005, at 6:34 AM, Tetsuro KURITA wrote:

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.
`

In generaly,
inv(a*b) \= inv(b)*inv(a)

`If both of a and b are nonsingular matrixes, the following equation is
``right.
`inv(a*b) = inv(b)*inv(a)
Acutually, in some case, polyfit.m give bad result.

`Please check if wpolyfit works better for you. I tested it using the
``NIST Statistical Reference Datasets
``(http://www.itl.nist.gov/div898/strd/). See
``octave-forge/main/optim/test_polyfit.m for details.
`

`wpolyfit gives a similar fit to polyfit but does a better job of
``estimating the uncertainty. In any case, the results are generally
``accurate to 10^-9 or better relative error.
`
I tried your formula in wsolve (from octave-forge):
x = inv(A'*A)*(A'*y);
and the results were worse, particularly on the Filippelli test.

`If you have a dataset for which polyfit performs particularly poorly
``please post it to the list.
`
Thanks,
- Paul
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**Problem of polyfit**, *Tetsuro KURITA*, `2005/10/06`
**Re: Problem of polyfit**, *Paul Kienzle*, `2005/10/06`
**Re: Problem of polyfit**, *Tetsuro KURITA*, `2005/10/06`
**Re: Problem of polyfit**,
*Paul Kienzle* **<=**
**Re: Problem of polyfit**, *Tetsuro KURITA*, `2005/10/06`
**Re: Problem of polyfit**, *Dmitri A. Sergatskov*, `2005/10/07`
**Re: Problem of polyfit**, *Tetsuro KURITA*, `2005/10/07`
**Re: Problem of polyfit**, *Fredrik Lingvall*, `2005/10/07`
**Re: Problem of polyfit**, *Tetsuro KURITA*, `2005/10/07`
**Re: Problem of polyfit**, *Paul Kienzle*, `2005/10/07`
**Re: Problem of polyfit**, *Fredrik Lingvall*, `2005/10/07`
**Re: Problem of polyfit**, *Paul Kienzle*, `2005/10/07`

**Re: Problem of polyfit**, *Fredrik Lingvall*, `2005/10/06`
**Re: Problem of polyfit**, *Dmitri A. Sergatskov*, `2005/10/07`