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arXiv · 0811.2365

Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations

Ronan Quarez
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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.

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Ronan Quarez. 2008-11-14. Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations. https://arxiv.org/abs/0811.2365

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