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Improving the domain of parameters for Newton's method with applications
(Journal of Computational and Applied Mathematics, 2017-07)
We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are ...
Local convergence of a relaxed two-step Newton like method with applications
(Journal of Mathematical Chemistry, 2017-08)
We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fr,chet derivative ...
New improved convergence analysis for Newton-like methods with applications
(Journal of Mathematical Chemistry, 2017-08)
We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases ...
Developments on the convergence of some iterative methods
(Optimization and Dynamics with Their Applications: Essays in Honor of Ferenc Szidarovszky, 2017)
Iterative methods, play an important role in computational sciences. In this chapter, we present new semilocal and local convergence results for the Newton-Kantorovich method. These new results extend the applicability of ...