Polynomial interpolation....
Nathann Cohen
I recently asked a question here : I have a set of points in R^n (or
C^n, or any vectorial space for the matter..), to which is associated
a set of values. Said differently, I have a function whose values I
only know at several points. I then would like, given a degree d, to
find a polynomial function of maximum degree d that goes through all
these points.
As Jason mentionned it in
http://groups.google.com/group/sage-support/browse_thread/thread/fa4a2936571de92f/a04de428e88abd77#a04de428e88abd77,
it seems to be the Chebyshev approximation defined in
http://mpmath.googlecode.com/svn/tags/0.13/doc/build/calculus/approximation.html.
Well, this approximation actually only works for dimension 1, while I
needed it in higher dimension. I wrote this functions, which is
basically the inversion of a matrix once everything is defined, and
thought it could be good to have it in Sage. Sadly, I know next to
nothing in this field of mathematics, and I am not sure my code is
clever/optimal. Besides, what is the best option ? Include it in
MPMaths ( fron which Jason found the approximation, or directly into
Sage ? )
Thank you for your help !
Nathann
Martin Rubey
We have a *very* efficient (well, I believe so, at least) version of
(generalized) one-dimensional rational interpolation in FriCAS, and it's
one of the very short term goals to adapt it for several dimensions.
Hm, if your values are in the ground field, it should be there already,
actually. In case of interest, I would check.
Help appreciated,
Martin