In this paper we study the problem of analyzing the convergence both local and semilocal of inexact Newton-like methods for approximating the solution of an equation in which there exists nondifferentiability. We will impose conditions, to ensure that the method converges, are weaker than in the ones imposed in previous results. The theoretical results shown in this study are applied to a chemical application in order to be proven.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space. J. Math. Anal. Appl. 298, 374–397 (2004)
I.K. Argyros, in Computational Theory of Iterative Methods, 15th edn., Studies in Computational Mathematics, ed. by C.K. Chui, L. Wuytack (Elsevier, New York, 2007)
I.K. Argyros, Á.A. Magreñán, Iterative Methods and Their Dynamics with Applications: A Contemporary Study (CRC Press, Boca Raton, 2017)
I.K. Argyros, S. Hilout, Computational Methods in Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications (World Scientific, Hackensack, 2013)
I.K. Argyros, Á.A. Magreñán, On the convergence of inexact two-point Newton-like methods on Banach spaces. Appl. Math. Comput. 265, 893–90293 (2015)
I.K. Argyros, S. Hilout, Numerical Methods in Nonlinear Analysis (World Scientific, Hackensack, 2013)
E. Cătinaş, The inexact, inexact perturbed, and quasi-Newton methods are equivalent models. Math. Comput. 74(249), 291–301 (2005)
J.E. Dennis, On Newton-like methods. Numer. Math. 11, 324–330 (1968)
P. Deuflhard, Newton Methods for Nonlinear Problems Affine Invariance and Adaptive Algorithms (Springer, Berlin, 2011)
M.Á. Hernández, N. Romero, On a characterization of some Newton-like methods of \(R\)-order at least three. J. Comput. Appl. Math. 183, 53–66 (2005)
L.V. Kantorovich, G.P. Akilov, Functional Analysis (Pergamon Press, Oxford, 1982)
Á.A. Magreñán, I.K. Argyros, A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications (Elsevier, New York, 2017)
J.M. Ortega, W.C. Rheinboldt, Iterative Solution of Nonlinear Equation in Several Variables (Academic Press, New York, 1970)
F.A. Potra, V. Pták, Nondiscrete Induction and Iterative Processes (Pitman, New York, 1984)
J.F. Traub, Iterative Method for Solutions of Equations (Prentice-Hall, Upper Saddle River, 1964)
T. Yamamoto, A convergence theorem for Newton-like methods in Banach spaces. Numer. Math. 51, 545–557 (1987)
Research supported in part by Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by Spanish MINECO Project PGC2018-095896-B-C21.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Argyros, I.K., Magreñán, Á.A., Moreno, D. et al. Weaker conditions for inexact mutitpoint Newton-like methods. J Math Chem 58, 706–716 (2020). https://doi.org/10.1007/s10910-020-01101-w
- Inexact Newton-like methods
- Unified convergence
- Nondifferentiable equation
- Weaker conditions