7 citations · 13 across the 12 of their papers we have counts for
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Piecewise Certificates of Positivity for matrix polynomials
Ronan Quarez
We show that any symmetric positive definite homogeneous matrix polynomial admits a piecewise semi-certificate, i.e. a collection of identites $M(…
On positive Matrices which have a Positive Smith Normal Form
Ronan Quarez
It is known that any symmetric matrix with entries in and which is positive semi-definite for any substitution of , has a Smith normal form whose diagonal coeff…
Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations
Ronan Quarez
First, we show that Sturm algorithm and Sylvester algorithm, which compute the number of real roots of a given univariate polynomial, lead to two dual tridiagonal determinantal rep…
Représentations déterminantales effectives des polynômes univariés par les matrices flèches
Ronan Quarez
We first show the existence of an effective determinantal representation for any univariate polynomial with real coefficients. Then, we more precisely establish that any univariate…