[Numpy-discussion] roots and high-order polynomial

[Fabrice Silva]

Le vendredi 03 juillet 2009 à 10:00 -0600, Charles R Harris a écrit :

> What do you mean by erratic? Are the computed roots different from
> known roots? The connection between polynomial coefficients and
> polynomial values becomes somewhat vague when the polynomial degree
> becomes large, it is numerically ill conditioned.

For an illustration of what I mean by 'erratic', see
http://fsilva.perso.ec-marseille.fr/visible/script_als_nbmodes.png or
http://fsilva.perso.ec-marseille.fr/visible/script_als_nbmodes.pdf
with the real part of the roots on the left, and the imaginary part of
the right:
- for low orders (<26), a pair of complex conjugate roots appears when
the order of polynomial is increased (with a step equal to 2). As
expected in my physical application, their real parts are negative.
- for higher order (>=26), there is no more 'hermitian
symmetry' (complex conjugate solutions), and real parts become
positive...

The computation of the coefficients of the polynomial is out of topic, I
already checked it and there is no errors.

-- 
Fabrice Silva
Laboratory of Mechanics and Acoustics - CNRS
31 chemin Joseph Aiguier, 13402 Marseille, France.