2 papers
math.RA2008
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…
math.RA2008
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…