Results 21 to 30 of about 9,082,480 (262)
Convergence of Derivative-Free Iterative Methods with or without Memory in Banach Space
Foundations, 2023 A method without memory as well as a method with memory are developed free of derivatives for solving equations in Banach spaces. The convergence order of these methods is established in the scalar case using Taylor expansions and hypotheses on higher ...
Santhosh George +2 more
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Extended Convergence of Two Multi-Step Iterative Methods
Foundations, 2023 Iterative methods which have high convergence order are crucial in computational mathematics since the iterates produce sequences converging to the root of a non-linear equation. A plethora of applications in chemistry and physics require the solution of
Samundra Regmi +3 more
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On the convergence of Kurchatov-type methods using recurrent functions for solving equations
Математичні Студії, 2022 We study a local and semi-local convergence of Kurchatov's method and its two-step modification for solving nonlinear equations under the classical Lipschitz conditions for the first-order divided differences. To develop a convergence analysis we use the
I. K. Argyros, S. Shakhno, H. Yarmola
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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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Mathematics, 2022 This article is an independently written continuation of an earlier study with the same title [Mathematics, 2022, 10, 1225] on the Newton Process (NP). This process is applied to solve nonlinear equations. The complementing features are: the smallness of
Samundra Regmi +3 more
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Local Comparison between Two Ninth Convergence Order Algorithms for Equations
Algorithms, 2020 A local convergence comparison is presented between two ninth order algorithms for solving nonlinear equations. In earlier studies derivatives not appearing on the algorithms up to the 10th order were utilized to show convergence.
Samundra Regmi +2 more
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Mathematics, 2023 A novel local and semi-local convergence theorem for the four-step nonlinear scheme is presented. Earlier studies on local convergence were conducted without particular assumption on Lipschitz constant.
Akanksha Saxena +3 more
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Unified Convergence Analysis of Two-Step Iterative Methods for Solving Equations
European Journal of Mathematical Analysis, 2021 In this paper we consider unified convergence analysis of two-step iterative methods for solving equations in the Banach space setting. The convergence order four was shown using Taylor expansions requiring the existence of the fifth derivative not on ...
Ioannis K. Argyros
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Three-Step Derivative-Free Method of Order Six
Foundations, 2023 Derivative-free iterative methods are useful to approximate the numerical solutions when the given function lacks explicit derivative information or when the derivatives are too expensive to compute.
Sunil Kumar +3 more
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