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Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems

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Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems

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Nombre: Moreno;Saiz - Inverse ...
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dc.contributor.author Moreno Flores, Joaquín es_ES
dc.contributor.author Saiz Martinez, Andrés es_ES
dc.date.accessioned 2015-04-28T07:31:57Z
dc.date.available 2015-04-28T07:31:57Z
dc.date.issued 2011
dc.identifier.issn 1017-1398
dc.identifier.uri http://hdl.handle.net/10251/49340
dc.description.abstract In this paper we present a new algorithm for solving polynomial equations based on the Taylor series of the inverse function of a polynomial, fP(y). The foundations of the computing of such series have been previously developed by the authors in some recent papers, proceeding as follows: given a polynomial function y = P(x) = a0 + a1x +···+ amxm, with ai ∈ R, 0 ≤ i ≤ m, and a real number u so that P (u) = 0, we have got an analytic function fP(y) that satisfies x = fP(P(x)) around x = u. Besides, we also introduce a new proof (completely different) of the theorems involves in the construction of fP(y), which provide a better radius of convergence of its Taylor series, and a more general perspective that could allow its application to other kinds of equations, not only polynomials. Finally, we illustrate with some examples how fP(y) could be used for solving polynomial systems. This question has been already treated by the authors in preceding works in a very complex and hard way, that we want to overcome by using the introduced algorithm in this paper. es_ES
dc.language Español es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Numerical Algorithms es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Newton’s method es_ES
dc.subject Quasi-Newton methods es_ES
dc.subject Inverse function of polynomials es_ES
dc.subject Polynomial zeros es_ES
dc.subject Polynomial systems zeros es_ES
dc.subject Algorithms es_ES
dc.subject Nonlinear equations es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s11075-011-9453-x
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Moreno Flores, J.; Saiz Martinez, A. (2011). Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems. Numerical Algorithms. 58(2):203-233. doi:10.1007/s11075-011-9453-x es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1007/s11075-011-9453-x es_ES
dc.description.upvformatpinicio 203 es_ES
dc.description.upvformatpfin 233 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 58 es_ES
dc.description.issue 2 es_ES
dc.relation.senia 41424
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