Weaker conditions for the convergence of Newton's method

Authors:
Ioannis K. Argyros;Saïd Hilout
Affiliations:
Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA;Poitiers University, Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France
Venue:
Journal of Complexity
Year:
2012

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Abstract

Newton's method is often used for solving nonlinear equations. In this paper, we show that Newton's method converges under weaker convergence criteria than those given in earlier studies, such as Argyros (2004) [2, p. 387], Argyros and Hilout (2010)[11, p. 12], Argyros et al. (2011) [12, p. 26], Ortega and Rheinboldt (1970) [26, p. 421], Potra and Ptak (1984) [36, p. 22]. These new results are illustrated by several numerical examples, for which the older convergence criteria do not hold but for which our weaker convergence criteria are satisfied.