# Lower bounds for univariate real polynomials

Ignacio García-Marco
I2M, Aix-Marseille Université

Date(s) : 28/09/2017   iCal
11 h 00 min - 12 h 00 min

In this talk, we consider real univariate polynomials and we study their representations as sums of powers of degree 1 polynomials. The goal of this talk is to present families of polynomials such that the number of terms required in such a representation is of order d. This is clearly optimal up to a constant factor. Previous lower bounds for this problem were only of order $\sqrt{d}$. We obtain this improvement thanks to a link of this problem with the problem of real Birkhoff interpolation.

This talk is based on a joint work with Pascal Koiran: Lower bounds by Birkhoff interpolation. Journal of Complexity 39 (2017), 38-50.

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