Results 21 to 30 of about 470,890 (244)
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 Semi-Local Convergence of a Noor–Waseem-like Method for Nonlinear Equations
Foundations, 2022 The significant feature of this paper is that the semi-local convergence of high order methods for solving nonlinear equations defined on abstract spaces has not been studied extensively as done for the local convergence by a plethora of authors which is certainly a more interesting case.
Ioannis K. Argyros +3 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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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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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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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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Unified Semi-Local Convergence for k—Step Iterative Methods with Flexible and Frozen Linear Operator [PDF]
Mathematics, 2018 The aim of this article is to present a unified semi-local convergence analysis for a k-step iterative method containing the inverse of a flexible and frozen linear operator for Banach space valued operators. Special choices of the linear operator reduce the method to the Newton-type, Newton’s, or Stirling’s, or Steffensen’s, or other methods.
Ioannis K. Argyros, Santhosh George
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Mathematics, 2022 Numerous three-step methods of high convergence order have been developed to produce sequences approximating solutions of equations usually defined on the Euclidean space with a finite dimension.
Ramandeep Behl +3 more
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Extended Kung–Traub Methods for Solving Equations with Applications
Mathematics, 2021 Kung and Traub (1974) proposed an iterative method for solving equations defined on the real line. The convergence order four was shown using Taylor expansions, requiring the existence of the fifth derivative not in this method. However, these hypotheses
Samundra Regmi +4 more
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