Lower Bounds by Birkhoff Interpolation - ENS de Lyon - École normale supérieure de Lyon Access content directly
Journal Articles Journal of Complexity Year : 2017

Lower Bounds by Birkhoff Interpolation

Abstract

In this paper we give lower bounds for the representation of real univariate polynomials as sums of powers of degree 1 polynomials. We present two families of polynomials of degree d such that the number of powers that are required in such a representation must be at least of order d. This is clearly optimal up to a constant factor. Previous lower bounds for this problem were only of order Ω(√ d), and were obtained from arguments based on Wronskian determinants and "shifted derivatives." We obtain this improvement thanks to a new lower bound method based on Birkhoff interpolation (also known as "lacunary polynomial interpolation").
Fichier principal
Vignette du fichier
birkhoff.arxiv.pdf (241.64 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

ensl-01172296 , version 1 (07-07-2015)

Identifiers

Cite

Ignacio Garcia-Marco, Pascal Koiran. Lower Bounds by Birkhoff Interpolation. Journal of Complexity, 2017. ⟨ensl-01172296⟩
45 View
414 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More