Problem with expand in lagrange interpolation

By expanding a high degree polynomial we typically create a
numerically unstable result, since the first term begins to dominate
rapidly, among other things.

The newton divided difference formula is designed to avoid that, I
think it's the same thing as the horner scheme that we get from
"horner" in maxima

http://en.wikipedia.org/wiki/Lagrange_interpolation
http://en.wikipedia.org/wiki/Newton_polynomial
http://en.wikipedia.org/wiki/Horner_scheme

so perhaps instead of "expand" try applying "horner"

-- 
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan