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FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

Akritas, Alkiviadis, Argyris, Andreas, Strzeboński, Adam (2008)

Serdica Journal of Computing

In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate...

Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

Iliev, Anton (1998)

Serdica Mathematical Journal

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.

Inégalités sur la mesure de Mahler d'un polynôme

V. Flammang (1997)

Journal de théorie des nombres de Bordeaux

Dans cet article, nous donnons une minoration de la mesure de Mahler d'un polynôme à coefficients entiers, dont toutes les racines sont d'une part réelles positives, d'autre part réelles, en fonction de la valeur de ce polynôme en zéro. Ces minorations améliorent des résultats antérieurs de A. Schinzel. Par ailleurs, nous en déduisons des inégalités de M.-J. Bertin, liant la mesure d'un nombre algébrique à sa norme.

Introduction to Rational Functions

Christoph Schwarzweller (2012)

Formalized Mathematics

In this article we formalize rational functions as pairs of polynomials and define some basic notions including the degree and evaluation of rational functions [8]. The main goal of the article is to provide properties of rational functions necessary to prove a theorem on the stability of networks

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