[SciPy-dev] Difference between polynomial.trimcoef and trimseq
Charles R Harris
Sun Jan 24 08:55:02 CST 2010
On Sun, Jan 24, 2010 at 12:44 AM, Anne Archibald
> 2010/1/24 David Goldsmith <firstname.lastname@example.org>:
> > PS: If I were to use chebyshev as my "template," what would you say is
> > next most useful/algorithmically-studied polynomial basis to implement?
> There was extensive (and occasionally heated) discussion of other
> polynomial representations around the time the Chebyshev routines were
> being introduced. My point of view in that discussion was that there
> should be a general framework for working with polynomials in many
> representations, but the representations I thought might be worth
> having were:
> (a) Power basis.
> (b) Chebyshev basis.
> (c) Bases of other families of orthogonal polynomials.
> (d) Lagrange basis (polynomials by value).
> (e) Spline basis.
> The need for polynomials expressed in terms of other families of
> orthogonal polynomials is to some degree alleviated by the improved
> orthogonal polynomial support that came in a little after the
> discussion. Polynomials by value are a useful tool; if you choose the
> right evaluation points they are competitive with Chebyshev
> polynomials for many purposes, and they can do other things as well.
Speaking of polynomials by value, I have some (cython) routines for
barycentric interpolation of trigonometric polynomials I wanted to add to
your barycentric work but it seemed that some reorganization of the
interpolation folder with maybe some renaming might be in order. I was
thinking of a separate barycentric folder. Also, I think the name polyint
could maybe be changed to something more suggestive of the contents.
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