Results 11 to 20 of about 900 (183)

On the semilocal convergence of efficient Chebyshev–Secant-type methods [PDF]

Journal of Computational and Applied Mathematics, 2011
We introduce a three-step ChebyshevSecant-type method (CSTM) with high efficiency index for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for (CSTM) using recurrence relations. Numerical examples validating our theoretical results are also provided in this study. © 2011 Elsevier B.V.
Ioannis K. Argyros, J. A. Ezquerro, José Manuel Gutiérrez Jiménez, Miguel Ángel Hernández-Verón, Saïd Hilout   +4 more
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Semilocal convergence of the secant method under mild convergence conditions of differentiability [PDF]

Computers & Mathematics with Applications, 2002
In this work, we obtain a semilocal convergence result for the secant method in Banach spaces under mild convergence conditions. We consider a condition for divided differences which generalizes those usual ones, i.e., Lipschitz continuous and Hölder continuous conditions. Also, we obtain a result for uniqueness of solutions.
Hernández, M.A., Rubio, M.J.
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Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method

Journal of Computational and Applied Mathematics, 2000
This study obtains two semilocal convergence results for the well-known Chebyshev method, which is a third-order iterative process. The hypotheses required are modifications to the normal Kantorovich ones. The results obtained are applied to the reduction of nonlinear integral equations of the Fredholm type and first kind.
Hernández, M.A., Salanova, M.A.
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Extended sufficient semilocal convergence for the Secant method

Computers & Mathematics with Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yeol Je Cho, Ioannis K. Argyros, Saïd Hilout   +2 more
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Semilocal convergence of a family of iterative methods in Banach spaces [PDF]

Numerical Algorithms, 2013
This work has been supported by Ministerio de Ciencia e Innovaci´on MTM2011-28636-C02-02 and by Vicerrectorado de Investigaci´on.
José L. Hueso, Eulalia Martínez
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A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces

Mathematics, 2022
To deal with the estimation of the locally unique solutions of nonlinear systems in Banach spaces, the local as well as semilocal convergence analysis is established for two higher order iterative methods. The given methods do not involve the computation
Janak Raj Sharma, Harmandeep Singh, Ioannis K. Argyros   +2 more
doaj   +2 more sources

Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition [PDF]

Abstract and Applied Analysis, 2012
Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented.
Xiubin Xu, Yuan Xiao, Tao Liu
doaj   +2 more sources

Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena

Journal of Numerical Analysis and Approximation Theory
In this work, a comprehensive analysis of a multi-step iterative composition for nonlinear equation is performed, providing insights into both local and semilocal convergence properties.
Sunil Kumar, Janak Raj Sharma, Ioannis K. Argyros   +2 more
doaj   +3 more sources

Semilocal Convergence Domain of a Chandrasekhar Integral Equation

Symmetry
In this study, we discuss the semilocal convergence analysis of a fourth-order iterative method in Banach spaces. We assume the Fréchet derivative satisfies the Lipschitz continuity condition, obtains suitable recurrence relations, and determines the domain of convergence under appropriate initial estimates.
Eulalia Martínez, Arleen Ledesma
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A Semilocal Convergence for a Uniparametric Family of Efficient Secant-Like Methods [PDF]

Journal of Function Spaces, 2014
We present a semilocal convergence analysis for a uniparametric family of efficient secant-like methods (including the secant and Kurchatov method as special cases) in a Banach space setting (Ezquerro et al., 2000–2012). Using our idea of recurrent functions and tighter majorizing sequences, we provide convergence results under the same or less ...
Argyros, I.K., González, D., Magreñán, Á.A.   +2 more
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