Newton-like algorithms for kth root calculation
Marek Kuczma, Halina Światak (1991)
Annales Polonici Mathematici
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Marek Kuczma, Halina Światak (1991)
Annales Polonici Mathematici
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T.J. Ypma (1984)
Numerische Mathematik
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Herceg, Djordje, Herceg, Dragoslav (2008)
Novi Sad Journal of Mathematics
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Kyurkchiev, Nikolay, Iliev, Anton (2009)
Serdica Journal of Computing
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This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv. In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence. ...
Ioannis K. Argyros, Saïd Hilout (2013)
Czechoslovak Mathematical Journal
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We extend the applicability of Newton's method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Pták. We obtain new sufficient convergence conditions for Newton's method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F. A. Potra, V. Pták, Sharp error bounds for Newton's process, Numer. Math., 34 (1980), 63–72, and F. A. Potra,...
Sahari, M.L., Djellit, I. (2006)
Discrete Dynamics in Nature and Society
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Ioannis K. Argyros, Saïd Hilout (2010)
Applicationes Mathematicae
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We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained. Furthermore,...
Florian-Alexandru Potra, Vlastimil Pták (1983)
Časopis pro pěstování matematiky
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Ioannis K. Argyros (2005)
Applicationes Mathematicae
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The Newton-Kantorovich approach and the majorant principle are used to provide new local and semilocal convergence results for Newton-like methods using outer or generalized inverses in a Banach space setting. Using the same conditions as before, we provide more precise information on the location of the solution and on the error bounds on the distances involved. Moreover since our Newton-Kantorovich-type hypothesis is weaker than before, we can cover cases where the original Newton-Kantorovich...