26/09/2014

Intervenant(s) : Aaron Herman (North Carolina State University & PolSys team, CNRS/INRIA/UPMC)

Let f be a square-free polynomial. The root separation of f is the minimum of the pair-wise distances between the complex roots of f. Finding a lower bound on the root separation is a fundamental problem, arising in numerous disciplines. Due to its importance, there has been extensive research on this problem, resulting in various bounds. In this talk, we present another bound, which is "nicer" than the previous bounds in that (1) It is bigger (hence better) than the previous bounds. (2) It is covariant under the scaling of the roots, unlike the previous bounds (if the roots of f are all doubled, the bound is doubled.) We will also talk about how to derive a similarly "nice" root separation bound for square-free polynomial systems.

Joint work with Hoon Hong and Elias Tsigaridas.

Elias.Tsigaridas (at) nulllip6.fr