Results 11 to 20 of about 16,081 (276)
The Convergence Ball and Error Analysis of the Relaxed Secant Method [PDF]
Advances in Mathematical Physics, 2017 A relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order.
Rongfei Lin +3 more
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Ball convergence for an Aitken-Newton method
Journal of Numerical Analysis and Approximation Theory, 2018 We present a local convergence analysis of an eighth-order Aitken-Newton method for approximating a locally unique solution of a nonlinear equation. Earlier studies have shown convergence of these methods under hypotheses up to the eighth derivative of ...
Ioannis K. Argyros +2 more
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Ball Convergence for Steffensen-type Fourth-order Methods [PDF]
International Journal of Interactive Multimedia and Artificial Intelligence, 2015 We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation.
Ioannis K. Argyros, Santhosh George
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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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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 ...
Guan, Lei +5 more
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Convergence rates of the Heavy-Ball method under the Lojasiewicz property
Mathematical Programming, 2023 International audienceIn this paper, a joint study of the behavior of solutions of the Heavy Ball ODE and Heavy Ball type algorithms is given. Since the pioneering work of B.T.
Dossal, Charles +2 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.
José A. Ezquerro +1 more
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Local Convergence of Newton’s Method on Lie Groups and Uniqueness Balls [PDF]
Abstract and Applied Analysis, 2013 An estimation of uniqueness ball of a zero point of a mapping on Lie group is established. Furthermore, we obtain a unified estimation of radius of convergence ball of Newton’s method on Lie groups under a generalized L-average Lipschitz condition.
Jinsu He, Jinhua Wang, Jen-Chih Yao
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Computers and Mathematics With Applications, 2004 Under the hypotheses that nonlinear operators have (K, p)-Hölder-type continuous derivatives, exact estimates of the radius of the convergence ball of Newton's method and of the uniqueness ball of solution of equations are ...
Huang, Zhengda
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Enlarging the convergence ball of Newton's method on Lie groups [PDF]
Journal of Numerical Analysis and Approximation Theory, 2015 We present a local convergence analysis of Newton's method for approximating a zero of a mapping from a Lie group into its Lie algebra. Using more precise estimates than before [55, 56] and under the same computational cost, we obtain a larger ...
Ioannis K. Argyros, Saïd Hilout
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