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Author:I. K. Argyros , Á. A. Magreñán ...
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2017, Vol.55 (7), pp.1427-1442Springer
Abstract: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 Fréchet derivative and on the center divided-difference of order one are...
Author:I. K. Argyros , M. A. Hernández-Verón , M. J. Rubio
Data Source:[J].Numerical Algorithms(IF 1.128), 2017, Vol.75 (1), pp.229-244Springer
Abstract:We present a semilocal as well as a local convergence analysis of Steffensen’s method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The novelty of this paper is twofold. On the one hand, we show convergence under general...
Author:I. K. Argyros , J. A. Ezquerro ...
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2017, Vol.55 (7), pp.1392-1406Springer
Abstract:We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead of just Hölder conditions, for the first derivat...
Author:I. K. Argyros , Ramandeep Behl
Data Source:[J].Computational and Applied Mathematics(IF 0.413), 2018, Vol.37 (2), pp.1913-1940Springer
Abstract:Abstract(#br)In this work, we propose a higher-order derivative free family for solving non-linear systems. The local order of convergence of the constructed family is first determined using first-order divided difference operators for functions of several variables and dire...
Author:I. K. Argyros , J. J. Rainer
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2018, Vol.56 (7), pp.2117-2131Springer
Abstract:Abstract(#br)We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative or even higher. The convergence in this study...
Author:I. K. Argyros , Hongmin Ren
Data Source:[J].International Journal of Computer Mathematics(IF 0.542), 2013, Vol.90 (3), pp.691-704Taylor & Francis
Abstract:We introduce a Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting. Then, we present a local convergence analysis for (STTM) using recurrence relations. Numerical examples validating our theoretical results are also provided in this study ...
Author:I. K. Argyros , J. A. Ezquerro ...
Data Source:[J].Milan Journal of Mathematics(IF 0.467), 2013, Vol.81 (1), pp.25-35Springer
Abstract:Abstract(#br)In this paper we give a semilocal convergence theorem for a family of iterative methods for solving nonlinear equations defined between two Banach spaces. This family is obtained as a combination of the well known Secant method and Chebyshev method. We give a very ge...
Author:I. K. Argyros , D. González
Data Source:[J].Numerical Algorithms(IF 1.128), 2013, Vol.64 (3), pp.549-565Springer
Abstract:Abstract(#br)We present a unified approach to generating majorizing sequences for multipoint iterative procedures in order to solve nonlinear equations in a Banach space setting. The semilocal convergence results have the following advantages over earlier work (under the same com...
Author:I. K. Argyros
Data Source:[J].Computing(IF 0.807), 1990, Vol.45 (3), pp.265-268Springer
Abstract:Abstract(#br)In this note we extend the validity of the mesh-independence principle for nonlinear operator equations and their discretizations to include operators whose derivatives are only Hölder continuous.
Author:I. K. Argyros
Data Source:[J].Acta Mathematica Hungarica(IF 0.348), 1999, Vol.84 (3), pp.209-219Springer
Abstract:Abstract(#br)Using the majorant method we find sufficient conditions for the convergence of a Chebysheff-Halley-type method in a Banach space. Our results improve all our previous results as well as those of others.

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