Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions
Computation, 2020 The technique of using the restricted convergence region is applied to study a semilocal convergence of the Newton−Kurchatov method. The analysis is provided under weak conditions for the derivatives and the first order divided differences ...
Ioannis K. Argyros +2 more
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Fractal and Fractional, 2023 Local convergence of order three has been established for the Newton–Simpson method (NS), provided that derivatives up to order four exist. However, these derivatives may not exist and the NS can converge.
Santhosh George +4 more
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Semilocal convergence of secant-like methods for differentiable and nondifferentiable operator equations [PDF]
, 2013 From well-known secant-like methods, we observe that we can construct a new family of secant-like methods that includes the secant method and Kurchatov's method. We analyse the local orders of convergence and the efficiencies of the methods of the family
Ezquerro, J.A. [0000-0001-8120-167X] +3 more
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Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces
Complexity, 2018 The semilocal and local convergence analyses of a two-step iterative method for nonlinear nondifferentiable operators are described in Banach spaces. The recurrence relations are derived under weaker conditions on the operator. For semilocal convergence,
Abhimanyu Kumar +3 more
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Auxiliary point on the semilocal convergence of Newton’s method
Journal of Computational and Applied Mathematics, 2019 We use an auxiliary point in the analysis of the semilocal convergence of Newton’smethod under center conditions on high order derivatives of the operator involved anduse the majorant principle of Kantorovich to do it.
J. A. Ezquerro, M. A. Hernández-Verón
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A general semilocal convergence result for Newton's method under centered conditions for the second derivative [PDF]
, 2012 From Kantorovich’s theory we present a semilocal convergence result for Newton’s method which is based mainly on a modification of the condition required to the second derivative of the operator involved.
Hernández, Miguel Ángel +8 more
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A semilocal convergence analysis for directional Newton methods [PDF]
Mathematics of Computation, 2010 A semilocal convergence analysis for directional Newton methods in n n -variables is provided in this study.
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On Newton's method for subanalytic equations
Journal of Numerical Analysis and Approximation Theory, 2017 We present local and semilocal convergence results for Newton’s method in order to approximate solutions of subanalytic equations. The local convergence results are given under weaker conditions than in earlier studies such as [9], [10], [14], [15], [24]
Ioannis K. Argyros, Santhosh George
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Expanding the applicability of the Gauss-Newton method for a certain class of systems of equations
Journal of Numerical Analysis and Approximation Theory, 2016 We present a new semilocal convergence analysis of the Gauss-Newton method in order to solve a certain class of systems of equations under a majorant condition.
Ioannis K. Argyros, Santhosh George
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SEMI-LOCAL CONVERGENCE OF A DERIVATIVE-FREEMETHOD FOR SOLVING EQUATIONS
Проблемы анализа, 2021 We present the semi-local convergence analysis of atwo-step derivative-free method for solving Banach space valuedequations. The convergence criteria are based only on the firstderivative and our idea of recurrent functions.
Gus Argyros +3 more
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