Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4625630 | Applied Mathematics and Computation | 2016 | 10 Pages |
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.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Beatriz Campos, Antonio Garijo, Xavier Jarque, Pura Vindel,