[SciPy-dev] Generic polynomials class (was Re: Volunteer for Scipy Project)
Thu Oct 15 15:54:13 CDT 2009
2009/10/15 Charles R Harris <firstname.lastname@example.org>:
> I think it would be interesting to see an implementation restricted to
> Lagrange basis only and as simple as you could make it.
See the branch lagrangeonly in git. The simplification is not that
great, since Lagrange polynomials really need a Basis object to keep
the list of points they're defined on around. I'd also hope that there
was some way to identify all polynomial objects, since (for example) a
Lagrange polynomial can be multiplied with a polynomial in any
representation to give another Lagrange polynomial...
>> I'd argue, though, that a general, efficient, numerically-stable
>> polynomial class could replace KroghInterpolator and
>> BarycentricInterpolator and serve to make PiecewisePolynomial more
>> powerful, for example.
> I agree completely on this point. That is one reason I think a "simplest"
> class for Lagrange bases would be interesting to look at.
I'm not sure whether Lagrange polynomials alone would qualify - their
derivative and integral methods are kind of expensive, and they are
not necessarily the most stable available, even in barycentric form.
It's also not easy to impose derivative conditions on them, which is
needed for PiecewisePolynomial in many applications. This is why I was
thinking of multiple representations...
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