On Sun, Jan 24, 2010 at 12:44 AM, Anne Archibald <peridot.faceted@gmail.com>wrote:
2010/1/24 David Goldsmith <d.l.goldsmith@gmail.com>:
PS: If I were to use chebyshev as my "template," what would you say is the 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. Chuck