Local convergence for composite Chebyshev-type methods
Communications in Advanced Mathematical Sciences, 2018 We replace Chebyshev's method for solving equations requiring the second derivative by a Chebyshev-type second derivative free method. The local convergence analysis of the new method is provided using hypotheses only on the first derivative in contrast ...
Santhosh George, İoannis K Argyros
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Extended convergence analysis of Newton-Potra solver for equations
Journal of Numerical Analysis and Approximation Theory, 2020 In the paper a local and a semi-local convergence of combined iterative process for solving nonlinear operator equations is investigated. This solver is built based on Newton solver and has R-convergence order 1.839....
Ioannis Argyros +3 more
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On the Local convergence of two-step Newton type Method in Banach Spaces under generalized Lipschitz Conditions [PDF]
Mathematics, 2021 The motive of this paper is to discuss the local convergence of a two-step Newton-type method of convergence rate three for solving nonlinear equations in Banach spaces.
Akanksha Saxena, J. P. Jaiswal
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Local Convergence of Two Fifth Order Algorithms with Hölder Continuity Assumptions
International Journal For Multidisciplinary Research, 2023 In order to estimate the solution of the zero for the nonlinear systems, we conduct the local convergence investigation in this paper. In contrast to the Lipschitz condition used in the preceding study, we have used the Hölder continuity requirement ...
Mithun kumar Chaudhary +1 more
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Complete study of local convergence and basin of attraction of sixth-order iterative method
AIMS Mathematics, 2023 The local convergence analysis of the parameter based sixth-order iterative method is the primary focus of this article. This investigation was conducted based on the Fréchet derivative of the first order that satisfies the Lipschitz continuity condition.
K. Devi, P. Maroju
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Shearer's point process, the hard-sphere model and a continuum Lov\'asz Local Lemma [PDF]
, 2017 A point process is R-dependent, if it behaves independently beyond the minimum distance R. This work investigates uniform positive lower bounds on the avoidance functions of R-dependent simple point processes with a common intensity.
Hofer-Temmel, Christoph
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Unified Convergence Criteria of Derivative-Free Iterative Methods for Solving Nonlinear Equations
Computation, 2023 A local and semi-local convergence is developed of a class of iterative methods without derivatives for solving nonlinear Banach space valued operator equations under the classical Lipschitz conditions for first-order divided differences.
Samundra Regmi +3 more
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Two Point Iterative Schemes for Nondifferentiable Equations in Banach Space
European Journal of Mathematical Analysis, 2023 The local as well as the semi-local convergence analysis is established for a certain single step-two point iterative scheme defined on a Banach space setting. These schemes converge to a locally unique solution of a nonlinear equation.
Ioannis K. Argyros +2 more
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On the Local Convergence of a (p + 1)-Step Method of Order 2p + 1 for Solving Equations
Foundations, 2022 The local convergence of a generalized (p+1)-step iterative method of order 2p+1 is established in order to estimate the locally unique solutions of nonlinear equations in the Banach spaces.
J. Sharma +3 more
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Extended Local Convergence for the Chebyshev Method under the Majorant Condition
Asian Research Journal of Mathematics, 2022 In this article, we present the study on local convergence behaviour of Chebyshev's method, which is a third order iterative method used to solve a non-linear system in Banach space locale.
I. Argyros +3 more
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