15 citations · 20 across the 10 of their papers we have counts for
4 papers · 1 filter
On the complexity of partial derivatives
Ignacio Garcia-Marco, Pascal Koiran, Timothée Pecatte +1
The method of partial derivatives is one of the most successful lower bound methods for arithmetic circuits. It uses as a complexity measure the dimension of the span of the partia…
Reconstruction Algorithms for Sums of Affine Powers
Ignacio Garcia-Marco, Pascal Koiran, Timothée Pecatte
In this paper we study sums of powers of affine functions in (mostly) one variable. Although quite simple, this model is a generalization of two well-studied models: Waring decompo…
Lower Bounds by Birkhoff Interpolation
Ignacio Garcia-Marco, Pascal Koiran
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…
Log-concavity and lower bounds for arithmetic circuits
Ignacio García-Marco, Pascal Koiran, Sébastien Tavenas
One question that we investigate in this paper is, how can we build log-concave polynomials using sparse polynomials as building blocks? More precisely, let $f = \sum\_{i = 0}^d a\…