Opened Access The Newton Procedure for several variables


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Autor: Soto Prieto, Manuel Jesús
Vicente Córdoba, José Luis
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2011-07-15
Publicado en: Linear Algebra and its Applications, 435 (2), 255-269.
Tipo de documento: Artículo
Resumen: Let us consider an equation of the form P(x, z) = zm + w1(x)zm−1 + · · · + wm−1(x)z + wm(x) = 0, where m>1, n>1, x=(x1⋯xn) is a vector of variables, k is an algebraically closed field of characteristic zero, View the MathML source and wm(x)≠0. We consider representations of its roots as generalized Puiseux power series, obtained by iterating the classical Newton procedure for one variable. The key result of this paper is the following: Theorem 1.The iteration of the classical Newton procedure for one variable gives rise to representations of all the roots of the equation above by generalized Puiseux power series in x1/d, d∈Z>0, whose supports are contained in an n-dimensional, lex-positive strictly convex polyhedral cone (see Section 5). We must point out that the crucial result is not the existence of these representations, which is a well-known fact; but the fact that their supports are contained in such a special cone. We achieve the proof of this theorem by taking a suitable...
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Cita: Soto Prieto, M.J. y Vicente Córdoba, J.L. (2011). The Newton Procedure for several variables. Linear Algebra and its Applications, 435 (2), 255-269.
Tamaño: 226.8Kb
Formato: PDF


DOI: 10.1016/j.laa.2011.01.033

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