Title: Local convergence of Cauchy-type methods under hypotheses on the first derivative

Authors: I.K. Argyros; D. González

Addresses: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA ' Departamento de Matemática, Escuela Politécnica Nacional, Quito, Ecuador

Abstract: We present a local convergence analysis of Cauchy-type methods free of the second derivative using hypotheses only on the first derivative. In earlier studies such as Amat et al. (2003, 2008), Hernández and Salanova (1999), Jarratt (1996), Kou (2007), Parhi and Gupta (2007), Rall (1979) and Ren et al. (2009) hypotheses up to the fourth derivative have been used to show convergence although the method requires evaluations of the function and its derivative. This way we extend the applicability of these methods. Numerical examples are provided in this study where earlier results cannot apply but the new results can apply to solve equations.

Keywords: Cauchy's method; Newton's method; local convergence.

DOI: 10.1504/IJCVR.2017.087733

International Journal of Computational Vision and Robotics, 2017 Vol.7 No.6, pp.613 - 622

Received: 01 May 2015
Accepted: 12 Jun 2015
Published online: 01 Nov 2017 *

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