Newton method for symmetric quartic polynomial

descriptionPublicationkeyboard_double_arrow_right Article , Other ORP type 01 Nov 2016 Spain English Publisher:Elsevier BVJournal:Applied Mathematics and Computation, volume 290, pages 326-335 (issn: 0096-3003,

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Authors: Beatriz Campos; Antonio Garijo; Xavier Jarque; Pura Vindel;

doi: 10.1016/j.amc.2016.06.021

handle: 10234/161960 , 2445/108550

Newton method for symmetric quartic polynomial

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Abstract

We investigate the parameter plane of the Newton’s method applied to the family of quartic polynomials pa,b(z)=z4+az3+bz2+az+1,pa,b(z)=z4+az3+bz2+az+1, where a and b are real parameters. We divide the parameter plane (a,b)∈R2(a,b)∈R2 into twelve open and connected regions where p, p′ and p′′ have simple roots. In each of these regions we focus on the study of the Newton’s operator acting on the Riemann sphere. The authors would like to thank N. Fagella and J. Canela for their useful comments during the preparation of this manuscript. The third author is partially supported by the Polish NCN grant decision DEC-2012/06/M/ST1/00168. The second and third authors are supported by the Spanish project MTM2014-52209-C2-2-P and the Catalan project CIRIT 2014-SGR555.The first and the last authors are supported by the Spanish project MTM2014-52016-C02-2-P and UJI project P1.1B20115-16.

Country

Spain

Related Organizations

Autonomous University of Barcelona
Spain
University of Barcelona
Spain
Universitat Rovira i Virgili
Spain
Jaume I University
Spain

Keywords

Newton’s method, Sistemes dinàmics diferenciables, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets, Newton's method, holomorphic dynamics, Numerical computation of roots of polynomial equations, Julia and Fatou sets, Differentiable dynamical systems, Holomorphic dynamics

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