Results 31 to 40 of about 16,081 (276)
Fractal and Fractional, 2022 Under the same conditions, we propose the extended comparison between two derivative free schemes of order six for addressing equations. The existing convergence technique used the standard Taylor series approach, which requires derivatives up to order ...
Samundra Regmi +3 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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Extended High Order Algorithms for Equations under the Same Set of Conditions
Algorithms, 2021 A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order.
Ioannis K. Argyros +5 more
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Global convergence of the Heavy-ball method for convex optimization [PDF]
2015 European Control Conference (ECC), 2015 This paper establishes global convergence and provides global bounds of the convergence rate of the Heavy-ball method for convex optimization problems. When the objective function has Lipschitz-continuous gradient, we show that the Cesaro average of the iterates converges to the optimum at a rate of $O(1/k)$ where k is the number of iterations.
Euhanna Ghadimi +2 more
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Mathematical Problems in Engineering, 2019 The main contribution of this study is to present a new optimal eighth‐order scheme for locating zeros with multiplicity m ≥ 1. An extensive convergence analysis is presented with the main theorem in order to demonstrate the optimal eighth‐order convergence of the proposed scheme.
Ramandeep Behl +3 more
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Ball Convergence for eighth order method
, 2017 Consider the problem of approximating a locally unique solution x of the nonlinear equation F(x) = 0, (21.1) where F is a Fréchet-differentiable operator defined on a convex subset D of a Banach space X with values in a Banach space Y. The equation (21.1) covers wide range of problems in classical analysis and applications [1-30]. Closed form solutions
Argyros, Ioannis K +1 more
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Extending the Applicability of Newton’s Algorithm with Projections for Solving Generalized Equations
Applied System Innovation, 2020 A new technique is developed to extend the convergence ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in
Michael I. Argyros +4 more
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Heavy Ball Restarted CMRH Methods for Linear Systems
Mathematical and Computational Applications, 2018 The restarted CMRH method (changing minimal residual method based on the Hessenberg process) using fewer operations and storage is an alternative method to the restarted generalized minimal residual method (GMRES) method for linear systems.
Zhongming Teng, Xuansheng Wang
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Lubricants, 2023 The complex sliding behavior inside ball bearings seriously affects the mechanical system’s performance. Current dynamic models for predicting this behavior suffer from poor generality and convergence.
Shuaijun Ma +5 more
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On the Convergence of a Kurchatov-Type Method for Solving Nonlinear Equations and Its Applications
AppliedMathA local and a semi-local convergence analysis are presented for the Kurchatov-type method to solve numerically nonlinear equations in a Banach space. The method depends on a real parameter. By specializing the parameter, we obtain methods already studied
Ioannis K. Argyros +2 more
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