Malaysian Journal of Mathematical Sciences, December 2022, Vol. 16, No. 4
Third Order Root-Finding Methods based on a Generalization of Gander's Result
Sonia Busquier, José M. Gutiérrez2, and Higinio Ramos
Corresponding Email: higra@usal.es
Received date: 26 June 2022
Accepted date: 27 November 2022
Abstract:
In this paper, a generalization of a classical result by Gander concerning the characterization of third-order methods is addressed. New and classical methods are included in the family. In particular, a new construction of the well-known Chebyshev method is presented. Other methods, based on exponential and logarithmic fittings respectively, are rediscovered too. The proposed methods have a local cubic order of convergence and can be competitive with other third-order methods in the literature, as can be seen from the numerical examples presented.
Keywords: Nonlinear equations; root-finding method; exponential fitting approach; logarithmic fitting approach
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