Condition-based Low-Degree Approximation of Real Polynomial Systems I: The Zero-Dimensional Case
Résumé
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.
Domaines
Calcul formel [cs.SC]
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Condition_based_bounds_on_the_size_of_a_polynomial_zero_set_I.pdf (590)
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