Results 1 to 10 of about 13,410 (248)
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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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 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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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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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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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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Enlarging the convergence ball of Newton's method on Lie groups
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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Ball convergence for Traub-Steffensen like methods in Banach space [PDF]
Annals of the West University of Timisoara: Mathematics and Computer Science, 2015 We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies such as [16, 23] Taylor expansions and hypotheses up to the third
Argyros Ioannis K., George Santhosh
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Extended convergence analysis of Newton-Potra solver for equations
Journal of Numerical Analysis and Approximation Theory, 2020 In the paper a local and a semi-local convergence of combined iterative process for solving nonlinear operator equations is investigated. This solver is built based on Newton solver and has R-convergence order 1.839....
Ioannis Argyros +3 more
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Dimension-Independent Convergence Rate for Adagrad with Heavy-Ball Momentum
MathematicsIn this study, we analyze the convergence rate of Adagrad with momentum for non-convex optimization problems. We establish the first dimension-independent convergence rate under the (L0,L1)-smoothness assumption, which is a generalization of the standard
Kyunghun Nam, Sejun Park
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