Weaker conditions for the convergence of Newton’s method |
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| Authors: | Ioannis K. Argyros,Saï d Hilout |
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| Affiliation: | 1. Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA;2. Poitiers University, Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France |
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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 Pták (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. |
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| Keywords: | Newton&rsquo s method Banach space Rate of convergence Semi-local convergence Kantorovich&rsquo s hypothesis |
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