Results 11 to 20 of about 14,159 (238)
Mathematics, 2022 In the given study, we investigate the three-step NTS’s ball convergence for solving nonlinear operator equations with a convergence order of five in a Banach setting.
Akanksha Saxena +3 more
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The Newtonian Operator and Global Convergence Balls for Newton’s Method [PDF]
Mathematics, 2020 We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.
Ezquerro, José A. +3 more
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Ball Comparison between Two Efficient Weighted-Newton-like Solvers for Equations
Foundations, 2022 We compare the convergence balls and the dynamical behaviors of two efficient weighted-Newton-like equation solvers by Sharma and Arora, and Grau-Sánchez et al.
Ioannis K. Argyros +3 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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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
doaj +1 more source
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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Non-Ergodic Convergence Analysis of Heavy-Ball Algorithms
Proceedings of the AAAI Conference on Artificial Intelligence, 2019 In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions.
Tao Sun 0005 +5 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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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
doaj +1 more source
Multistep Iterative Methods for Solving Equations in Banach Space
MathematicsThe novelty of this article lies in the fact that we extend the use of a multistep method for developing a sequence whose limit solves a Banach space-valued equation. We suggest the error estimates, local convergence, and semi-local convergence, a radius
Ramandeep Behl +4 more
doaj +1 more source