Newton's method in Riemannian manifolds
Journal of Numerical Analysis and Approximation Theory, 2008 Using more precise majorizing sequences than before [1], [8], and under the same computational cost, we provide a finer semilocal convergence analysis of Newton's method in Riemannian manifolds with the following advantages: larger convergence domain ...
Ioannis K. Argyros
doaj +2 more sources
Using decomposition of the nonlinear operator for solving non‐differentiable problems
Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7987-8006, 15 May 2025.Starting from the decomposition method for operators, we consider Newton‐like iterative processes for approximating solutions of nonlinear operators in Banach spaces. These iterative processes maintain the quadratic convergence of Newton's method.
Eva G. Villalba +3 more
wiley +1 more source
Semilocal and local convergence of a fifth order iteration with Frechet derivative satisfying Holder condition [PDF]
, 2016 The semilocal and local convergence in Banach spaces is described for a fifth order iteration for the solutions of nonlinear equations when the Frechet derivative satisfies the Holder condition.
Singh, S. +3 more
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Memristive InAs‐Based Semiconductors with Anisotropic Ion Transport
Advanced Materials, Volume 37, Issue 20, May 19, 2025.Memristive semiconductor HxNa2‐xIn2As3 exhibits memristive switching and maintains semiconductor properties through ion migration in its vdW gaps. Low ion migration energy enables a low set voltage, while its low‐symmetry structure produces anisotropic ion transport, offering insights into directional dependence.
Taeyoung Kim +19 more
wiley +1 more source
Semilocal Convergence Analysis for MMN-HSS Methods under Hölder Conditions
, 2017 Multi-step modified Newton-HSS (MMN-HSS) methods, which are variants of inexact Newton methods, have been shown to be competitive for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices. Previously, we established
Yang Li, Xue-Ping Guo
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Directional k-Step Newton Methods in n Variables and its Semilocal Convergence Analysis [PDF]
, 2018 [EN] The directional k-step Newton methods (k a positive integer) is developed for solving a single nonlinear equation in n variables. Its semilocal convergence analysis is established by using two different approaches (recurrent relations and recurrent ...
Abhimanyu Kumar +7 more
core +1 more source
On the semilocal convergence of inexact Newton methods in Banach spaces
, 2008 We provide two types of semilocal convergence theorems for approximating a solution of an equation in a Banach space setting using an inexact Newton method [I.K.
Ioannis K. Argyros, Argyros, Ioannis K.
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Expanding the applicability of Newton-Tikhonov method for ill-posed equations
Journal of Numerical Analysis and Approximation Theory, 2014 We present a new semilocal convergence analysis of Newton- Tikhonov methods for solving ill-posed operator equations in a Hilbert space setting. Using more precise majorizing sequences and under the same computational cost as in earlier studies such as [
Ioannis K. Argyros, Santhosh George
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Third-Order Newton-Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems
Abstract and Applied Analysis, 2014 We present a third-order method for solving the systems of nonlinear equations. This method is a Newton-type scheme with the vector extrapolation. We establish the local and semilocal convergence of this method.
Wen Zhou, Jisheng Kou
doaj +1 more source
Semilocal convergence of a Secant-type method under weak Lipschitz conditions in Banach spaces [PDF]
, 2018 [EN] The semilocal convergence of double step Secant method to approximate a locally unique solution of a nonlinear equation is described in Banach space setting. Majorizing sequences are used under the assumption that the first-order divided differences
Abhimanyu Kumar +7 more
core +1 more source