112 citations · 425 across the 52 of their papers we have counts for
5 papers · 1 filter
Univariate Rational Sums of Squares
Teresa Krick, Bernard Mourrain, Agnes Szanto
Given rational univariate polynomials f and g such that gcd(f, g) and f / gcd(f, g) are relatively prime, we show that g is non-negative on all the real roots of f if and only if g…
On the Effective Putinar's Positivstellensatz and Moment Approximation
Lorenzo Baldi, Bernard Mourrain
We analyse the representation of positive polynomials in terms of Sums of Squares. We provide a quantitative version of Putinar's Positivstellensatz over a compact basic semialgebr…
Newton-Type Methods For Simultaneous Matrix Diagonalization
Rima Khouja, Bernard Mourrain, Jean-Claude Yakoubsohn
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matr…
Tensor decomposition for learning Gaussian mixtures from moments
Rima Khouja, Pierre-Alexandre Mattei, Bernard Mourrain
In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data. We consider the problem of recovering Gauss…
Computing real radicals by moment optimization
Lorenzo Baldi, Bernard Mourrain
We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of, which is based on convex moment optimization. A truncated positive generi…