Fractional Newton-Raphson method
The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method t...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Pompeu Fabra |
| Repositorio: | Repositorio Digital de la UPF |
| OAI Identifier: | oai:repositori.upf.edu:10230/59958 |
| Acceso en línea: | http://hdl.handle.net/10230/59958 http://dx.doi.org/10.5121/mathsj.2021.8101 |
| Access Level: | acceso abierto |
| Palabra clave: | Newton-Raphson Method Fractional Calculus Fractional Derivative |
| Sumario: | The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method. |
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