Displaying similar documents to “Remark on a Newton-Moser type method”

Extending the applicability of Newton's method using nondiscrete induction

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,...

On the convergence of the secant method under the gamma condition

Ioannis Argyros (2007)

Open Mathematics

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We provide sufficient convergence conditions for the Secant method of approximating a locally unique solution of an operator equation in a Banach space. The main hypothesis is the gamma condition first introduced in [10] for the study of Newton’s method. Our sufficient convergence condition reduces to the one obtained in [10] for Newton’s method. A numerical example is also provided.