A. M. Archibald peridot.faceted at gmail.com
Fri Oct 13 14:55:30 CDT 2006

On 13/10/06, Charles R Harris <charlesr.harris at gmail.com> wrote:

> You can also get *much* better results if you scale the x interval to [0,1]
> as the problem will be better posed. For instance, with your data and a
> degree 10 fit I get  a condition number of about 2e7 when x is scaled to
> [0,1], as opposed to about 1e36 when left as is. The former yields a
> perfectly useable fit while the latter blows up. I suppose this could be
> built into the polyfit routine if one were only interested in polynomial
> fits of some sort, but the polynomial would have to carry around an offset
> and scale factor to make evaluation work.

[-1,1] would probably be even better, no?

> If Travis is interested in such a thing we could put together some variant
> of the polynomials that includes the extra data.

At this point you might as well use a polynomial class that can
accomodate a variety of bases for the space of polynomials - X^n,
(X-a)^n, orthogonal polynomials (translated and scaled as needed),
what have you.

I think I vote for polyfit that is no more clever than it has to be
but which warns the user when the fit is bad.

A. M. Archibald

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