Newton method for symmetric quartic polynomial

Beatriz Campos, Antonio Garijo, Xavier Jarque and Pura Vindel

Applied Mathematics and Computation, 2016, vol. 290, issue C, 326-335

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, where a and b are real parameters. We divide the parameter plane (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.

Keywords: Newton’s method; Holomorphic dynamics; Julia and Fatou sets (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:290:y:2016:i:c:p:326-335

DOI: 10.1016/j.amc.2016.06.021

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