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 +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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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
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Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena [PDF]
Journal of Numerical Analysis and Approximation TheoryIn 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 +2 more
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Semilocal Convergence Domain of a Chandrasekhar Integral Equation
SymmetryIn 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. +2 more
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A new semilocal convergence theorem for Newton's method [PDF]
Journal of Computational and Applied Mathematics, 1997 A new semilocal convergence theorem for Newton's method is established for solving a nonlinear equation F(x)=0, defined in Banach spaces. It is assumed that the operator F is twice Fréchet differentiable, and F″ satisfies a Lipschitz type condition. Results on uniqueness of solution and error estimates are also given.
JoséM Gutiérrez +2 more
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Semilocal Convergence of a Multi-Step Parametric Family of Iterative Methods
Symmetry, 2023 In this paper, we deal with a new family of iterative methods for approximating the solution of nonlinear systems for non-differentiable operators. The novelty of this family is that it is a m-step generalization of the Steffensen-type method by updating the divided difference operator in the first two steps but not in the following ones.
Eva G. Villalba +2 more
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Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces [PDF]
Journal of Applied Mathematics, 2011 We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are
Liang Chen, Chuanqing Gu, Yanfang Ma
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A highly accurate family of stable and convergent numerical solvers based on Daftardar–Gejji and Jafari decomposition technique for systems of nonlinear equations [PDF]
MethodsXThis study introduces a family of root-solvers for systems of nonlinear equations, leveraging the Daftardar–Gejji and Jafari Decomposition Technique coupled with the midpoint quadrature rule.
Sania Qureshi +4 more
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