%0 Journal Article
%T Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations
%A Ronan Quarez
%J Mathematics
%D 2008
%I arXiv
%X 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 representations of the polynomial. Next, we show that the number of real roots of a polynomial given by a tridiagonal determinantal representation is greater than the signature of this representation.
%U http://arxiv.org/abs/0811.2365v1