Communication Dans Un Congrès Année : 2024

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.
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hal-04902434 , version 1 (20-01-2025)

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  • HAL Id : hal-04902434 , version 1

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Josué Tonelli-Cueto, Elias Tsigaridas. Condition-based Low-Degree Approximation of Real Polynomial Systems I: The Zero-Dimensional Case. MEGA 2024 - Effective Methods in Algebraic Geometry, Jul 2024, Leipzig, Germany. ⟨hal-04902434⟩
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