Dynamics of Newton-like root finding methods
When exploring the literature, it can be observed that the operator obtained when applying Newton-like root finding algorithms to the quadratic polynomials z - c has the same form regardless of which algorithm has been used. In this paper, we justify why this expression is obtained. This is done by...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:281986 |
| Acesso em linha: | https://ddd.uab.cat/record/281986 https://dx.doi.org/urn:doi:10.1007/s11075-022-01474-w |
| Access Level: | acceso abierto |
| Palavra-chave: | Iterative methods Newton-like algorithms Complex dynamics of rational functions |
| Resumo: | When exploring the literature, it can be observed that the operator obtained when applying Newton-like root finding algorithms to the quadratic polynomials z - c has the same form regardless of which algorithm has been used. In this paper, we justify why this expression is obtained. This is done by studying the symmetries of the operators obtained after applying Newton-like algorithms to a family of degree d polynomials p(z) = z - c. Moreover, we provide an iterative procedure to obtain the expression of new Newton-like algorithms. We also carry out a dynamical study of the given generic operator and provide general conclusions of this type of methods. |
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