Dynamics of Newton-like root finding methods
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913641511518208 |
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| author | Campos, Beatriz Canela, Jordi Vindel, Pura |
| author_facet | Campos, Beatriz Canela, Jordi Vindel, Pura |
| contents | When exploring the literature, it can be observed that the operator obtained when applying \textit{Newton-like} root finding algorithms to the quadratic polynomials $z^2-c$ 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 $p(z)=z^d-c$. Moreover, we provide an iterative procedure to obtain the expression of new Newton-like algoritms. We also carry out a dynamical study of the given generic operator and provide general conclusions of this type of methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of Newton-like root finding methods Campos, Beatriz Canela, Jordi Vindel, Pura Numerical Analysis 65F10, 37F10, 30C10 When exploring the literature, it can be observed that the operator obtained when applying \textit{Newton-like} root finding algorithms to the quadratic polynomials $z^2-c$ 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 $p(z)=z^d-c$. Moreover, we provide an iterative procedure to obtain the expression of new Newton-like algoritms. We also carry out a dynamical study of the given generic operator and provide general conclusions of this type of methods. |
| title | Dynamics of Newton-like root finding methods |
| topic | Numerical Analysis 65F10, 37F10, 30C10 |
| url | https://arxiv.org/abs/2501.04645 |