On the local convergence of a family of two-step iterative methods for solving nonlinear equations

• Autores: Miquel Grau Sánchez , Miquel Noguera Batlle , José Luis Díaz Barrero
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 255, Nº 1, 2014, págs. 753-764
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.06.043
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• Resumen

  • A local convergence analysis for a generalized family of two step Secant-like methods with frozen operator for solving nonlinear equations is presented. Unifying earlier methods such as Secant�s, Newton, Chebyshev-like, Steffensen and other new variants the family of iterative schemes is built up, where a profound and clear study of the computational efficiency is also carried out. Numerical examples and an application using multiple precision and a stopping criterion are implemented without using any known root. Finally, a study comparing the order, efficiency and elapsed time of the methods suggested supports the theoretical results claimed.