Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations
Rings and Algebras
2008-11-17 v1
Abstract
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.
Cite
@article{arxiv.0811.2365,
title = {Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations},
author = {Ronan Quarez},
journal= {arXiv preprint arXiv:0811.2365},
year = {2008}
}