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...

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Detalles Bibliográficos
Autores: Torres Hernandez, Anthony, Brambila Paz, Fernando
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
Descripción
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.