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Journal Articles Journal of Complexity Year : 2017

Lower Bounds by Birkhoff Interpolation

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



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