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Expanding the applicability of two-point Newton-like methods under generalized conditions

Ioannis K. Argyros, Saïd Hilout (2013)

Applicationes Mathematicae

We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied....

Extending the applicability of Newton's method using nondiscrete induction

Ioannis K. Argyros, Saïd Hilout (2013)

Czechoslovak Mathematical Journal

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, V. Pták, Nondiscrete...

Finding linking sets.

Schechter, Martin, Tintarev, Kyril (2006)

International Journal of Mathematics and Mathematical Sciences

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