One-point Newton-type iterative methods: A unified point of view

Alicia Cordero Barbero ^[1] ; Cristina Jordán Lluch ^[1] ; Juan Ramón Torregrosa Sánchez ^[1]
1. [1] Universidad Politécnica de Valencia
  
  Universidad Politécnica de Valencia
  
  Valencia, España
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 275, Nº 1, 2015, págs. 366-374
Idioma: inglés
DOI: 10.1016/j.cam.2014.07.009
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Resumen
- In this paper, a unified point of view that includes the most of one-point Newton-type iterative methods for solving nonlinear equations is introduced. A simple idea to design iterative methods with quadratic or cubic convergence is also described. This idea is extended to construct one-point iterative methods of order four. In addition, several numerical examples are given to illustrate and compare different known methods and some introduced by using this unifying idea.