Special Session 186: Recent Advances in Symbolic Computation and Applications

Condition-based Low-Degree Approximation of Real Polynomial Systems. I: The Zero-Dimensional Case
Elias Tsigaridas
Inria Paris and Sorbonne University
France
Co-Author(s):    Josue Tonelli-Cueto
Abstract:
We provide new bounds on the number of real zeros of a (zero-dimensional) polynomial system in terms of the condition number of the system. In the probabilistic setting, this translates into new estimates on all the moments of the number of the real zeros of random polynomial systems, including Kac and KSS polynomial systems. Moreover, the provided bounds are robust: they do not require the Gaussian assumption.