Rate of convergence of a generalization of Newton's method |
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| Authors: | Y Benadada J P Crouzeix J A Ferland |
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| Institution: | (1) Départment de Mathématiques, Faculté des Sciences, Tetouan, Maroc;(2) Centre National de la Recherche Scientifique, Mathématiques Appliquées, Sciences, Unité Associée 1501, Aubière, France;(3) Department d'Informatique et de Recherche Opérationnelle, Université de Montréal, Montréal, Québec, Canada |
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| Abstract: | The Newton's method for finding the root of the equation  (t)=0 can be easily generalized to the case where is monotone, convex, but not differentiable. Then, the convergence is superlinear. The purpose of this note is to show that the convergence is only superlinear. Indeed, for all   (1, 2), we exhibit an example where the convergence of the iterates is exactly . |
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| Keywords: | Newton's method rate of convergence |
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