Dynamics of a family of rational operators of arbitrary degree
In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to redefine the parameters to prevent redundancies and un-boundedness of problematic parameters. After reparametrization, we o...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:257135 |
| Online Access: | https://ddd.uab.cat/record/257135 https://dx.doi.org/urn:doi:10.3846/mma.2021.12642 |
| Access Level: | Open access |
| Keyword: | Iterative methods Parameter planes Complex dynamics of rational functions |
| Summary: | In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to redefine the parameters to prevent redundancies and un-boundedness of problematic parameters. After reparametrization, we observe that these rational maps belong to a more general family O of degree n + k operators, which includes several other families of maps obtained from other numerical methods. We study the dynamics of O and discuss for which parameters n and k these operators would be suitable from the numerical point of view. |
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