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Convergence and Dynamics of a Higher-Order Method [PDF]
Symmetry, 2020 Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves some iterative method generating a sequence approximating the solution.
Alejandro Moysi +5 more
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The order convergence structure [PDF]
Indagationes Mathematicae, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jan Harm van der Walt +1 more
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Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence
Journal of Numerical Analysis and Approximation Theory, 2021 We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used.
Ioannis K. Argyros, Santhosh George
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First-Order Convergence and Roots [PDF]
Combinatorics, Probability and Computing, 2015 Nešetřil and Ossona de Mendez introduced the notion of first-order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether, if (Gi)i∈ℕ is a sequence of graphs with M being their first-order limit and v is a vertex of M, then there exists a sequence (vi)i∈ℕ of vertices such that the graphs Gi rooted at vi ...
Demetres Christofides, Daniel Král'
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I-Statistical Rough Convergence of Order α
Journal of New Theory, 2022 The aim of this paper is to define the concept of I-statistical (I-st) rough convergence of order α (0 < α ≤ 1). It proposes the concept of I-st bounded of order α.
Sevcan Bulut, Aykut Or
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Memory in a New Variant of King’s Family for Solving Nonlinear Systems
Mathematics, 2020 In the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King’s family with order four to solve nonlinear systems along with its convergence ...
Munish Kansal +3 more
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Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations
Axioms, 2023 In this paper, a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations is presented. After the convergence analysis, a study of the stability of this class is made using the tools of complex ...
Alicia Cordero +3 more
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About Convergence and Order of Convergence of Some Fractional Derivatives
Progress in Fractional Differentiation and Applications, 2022 In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ for p=1 and $p=\infty$ and we prove that for both Caputo and Caputo Fabrizio operators the order of ...
Roscani, Sabrina Dina +1 more
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On the Semi-Local Convergence of Two Competing Sixth Order Methods for Equations in Banach Space
Algorithms, 2022 A plethora of methods are used for solving equations in the finite-dimensional Euclidean space. Higher-order derivatives, on the other hand, are utilized in the calculation of the local convergence order. However, these derivatives are not on the methods.
Ioannis K. Argyros +3 more
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First order convergence of matroids [PDF]
European Journal of Combinatorics, 2017 The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini-Schramm convergence for sparse structures. It is known that every first order convergent sequence of graphs with bounded tree-depth can be represented by an analytic limit object called a limit modeling.
Frantisek Kardos +3 more
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