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Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
We study the local convergence of a method presented by Cordero et al. of convergence order at least five to approximate a locally unique solution of a nonlinear equation. These studies show the convergence under hypotheses ...
ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION
(Universidad Católica del Norte, Departamento de Matemáticas, 2008)
On the local convergence and the dynamics of Chebyshev–Halley methods with six and eight order of convergence
We study the local convergence of Chebyshev–Halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation. In Sharma (2015) (see Theorem 1, p. 121) the convergence ...
Local and Semi-local convergence for Chebyshev two point like methods with applications in different fields
The convergence is developed for a large class of Chebyshev-two point-like methods for solving Banach space valued equations. Both the local as well as the semi-local convergence is provided for these methods under general ...
Improved convergence analysis for Newton-like methods
We present a new semilocal convergence analysis for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in ...
Local convergence for multi-point-parametric Chebyshev–Halley-type methods of high
We present a local convergence analysis for general multi-point-Chebyshev-Halley-type methods (MMCHTM) of high convergence order in order to approximate a solution of an equation in a Banach space setting. MMCHTM includes ...
An Improved Convergence and Complexity Analysis for the Interpolatory Newton Method
(Universidad de La Frontera. Departamento de Matemática y EstadísticaUniversidade Federal de Pernambuco. Departamento de Matemática, 2010)
Asymptotic error distribution for the Euler scheme with locally Lipschitz coefficients
(Elsevier, 2020)
In traditional works on numerical schemes for solving stochastic differential equations (SDEs), the globally Lipschitz assumption is often assumed to ensure different types of convergence. In practice, this is often too ...
Study of a high order family: Local convergence and dynamics
The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a ...
A unified convergence analysis for secant-type methods
We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes he computation ...