Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations

Details Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations

2008-11-14

arxiv.org/abs/0811.2365v1

Mathematics

Rings and Algebras

Scientific paper

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.

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