Uma Versão do Teorema de Vincent

Jean Fernandes Barros

Abstract


Neste trabalho, apresentamos uma versão geométrica do teorema de Vincent, conforme Alesina e Galuzzi (2000). A versão
clássica, como em Vincent (1836); Akritas (1981); Alesina e Galuzzi (1998), é dada em termos de frações contínuas, e tem por
finalidade a obtenção de uma solução númerica para as equações algébricas. Para uma demonstração da versão geométrica do
teorema de Vincent, nós utilizamos os resultados de Ostrowski (1950).

Keywords


Teorema de Vincent; Regra de Sinais de Descartes; Transformações de Möbius

References


Ahlfors, L. V. (1949). Complex Analysis: an introduction to the theory of analytic functions of one complex variable. McGraw-Hill.

Akritas, A. G. (1978). A correction on a theorem by uspensky. Bull Soc Math Greece, (19), 278–285.

Akritas, A. G. (1979). On the solution of polynomial equations using continued fractions. Information Processing Letters, 9(4), 182–184.

Akritas, A. G. (1981). Vincent’s forgotten theorem, its extension and application. Comp & Maths with Appls, (7), 309–317.

Akritas, A. G. (1986). There is no "uspensky"method. In: Proceedings of the 1986 Symposium on Simbolic and Algebraic Computation, Waterloo, Ontario, Canada, pp. 88–90.

Akritas, A. G., Danielopoulos, S. D. (1978). On the forgotten theorem of mr. vincent. Historia Math, (5), 427–435.

Alesina, A., Galuzzi, M. (1998). A new proof of vincent’s theorem. L’Enseignement Matématique, 44, 219–256.

Alesina, A., Galuzzi, M. (1999). Addendum to the paper "a new proof of vincent’s theorem". L’Enseignement Matématique.

Alesina, A., Galuzzi, M. (2000). Vincent’s theorem from a modern point of view. Categorical Studies in Italy, Rendiconti del Circolo Matematico de Palermo, (Serie II, 64), 179–191.

Barros, J. F., Leandro, E. S. G. (2011). The set of degenerate central configurations in the planar restricted fourbody problem. SIAM Journal of Mathematical Analysis, (43), 634–661.

Barros, J. F., Leandro, E. S. G. (2014). Bifurcations and enumeration of classes of relative equilibria in the planar restricted four-body problem. SIAM Journal of Mathematical Analysis, (46-2), 1185–1203.

Descartes, R. (1637). La geometrie in discours de la methode. Dover.

Eigenwillig, A. (2008). Real root isolation for exact and approximate polynomials using descartes’s rule of signs. Tese de Doutorado, Saarland University.

Lagrange, J. P. (1808). Traite de la resolution des equations numeriques de tous les degres, avec des notes sur plusieurs points de la theorie des equations algebriques. Chez Courcier.

Leandro, E. S. G. (2003). Finiteness and bifurcations of some symetrical classes of central configurations. Arch Rational Mech Anal.

Leandro, E. S. G. (2006). On the central configurations of the planar restricted four-body problem. Journal of Differential Equations, (226), 323–351.

Obreschkoff, N. (1963). Verteilung und berechnung der nullstellen reeller polynome. VEB Deustscher Verlag der Wissenschaften.

Obreschkoff, N. (2003). Zeros of polynomials. Marin Drinov.

Ostrowski, A. M. (1939). Note sur les produits de series normales. Bulletin de la Société Royale des Sciences de Liége, pp. 458–468.

Ostrowski, A. M. (1950). Note on vincent’s theorem. The Annals of Mathematics, 52(3), 702–707.

Uspensky, J. V. (1948). Theory of equations. McGraw-Hill.

Vincent, A. J. (1836). Sur la resolution des equations numeriques. J Math Pures Appl, (1), 341–372.

Wang, X. (2004). A simple proof of descartes’s rule of signs. The American Mathematical Monthly, (111), 525– 526.




DOI: https://doi.org/10.5902/2179460X34758

Copyright (c) 2019 Ciência e Natura

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.