[SciPy-User] multidimensional polynomial fit

David Goldsmith d.l.goldsmith@gmail....
Sun Jun 13 20:10:52 CDT 2010


On Sun, Jun 13, 2010 at 4:01 PM, Oscar Gerardo Lazo Arjona <
algebraicamente@gmail.com> wrote:

> David Goldsmith <d.l.goldsmith <at> gmail.com> writes:
> > So the number of data _must_ equal the number of terms in the
> polynomial?
> (Anything else will be over- or under-determined and require either some
> sort of
> error minimizing fit.)  What's your use case; just curious.DG
>
> No, in general, the number of data points will be different than the number
> of
> terms in the polynomial.


In that case, in what sense are your answers "exact"?

DG


> For lower-dimmensional fits (in particular for
> dimension 1) the number of points is expected to be larger than the number
> of
> terms, but for higher dimmensional polynomials, the number of terms grows
> very
> fast, and will probably be larger than the number of points.
>
> At this point it works very slowly for dimmensions greater than 2.
> Adjusting a
> set of 125 4-tuples to a polynomial of degree 3 takes approximately 12
> seconds
> on my intel-core2duo laptop. Perhaps it would be wise to implement it in
> some
> compiled language. I am learning fotran right now, perhaps that would make
> it...
>
> Yes, I will take sage objects out of an eventual contribution to numpy.
>
> Oscar
>
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