13 Result(s)
within
Á. Alberto Magreñán
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Article
Weaker conditions for inexact mutitpoint Newton-like methods
In this paper we study the problem of analyzing the convergence both local and semilocal of inexact Newton-like methods for approximating the solution of an equation in which there exists nondifferentiability....
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Article
Secant-like methods for solving nonlinear models with applications to chemistry
We present a local as well a semilocal convergence analysis of secant-like methods under g eneral conditions in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting....
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Article
Extending the Mesh Independence For Solving Nonlinear Equations Using Restricted Domains
The mesh independence principle states that, if Newton’s method is used to solve an equation on Banach spaces as well as finite dimensional discretizations of that equation, then the behaviour of the discretiz...
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Article
New improved convergence analysis for Newton-like methods with applications
We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these metho...
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Article
Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions
We present a local convergence analysis of a two-point four parameter Jarratt-like method of high convergence order in order to approximate a locally unique solution of a nonlinear equation. In contrast to ear...
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Chapter
Developments on the Convergence of Some Iterative Methods
Iterative methods, play an important role in computational sciences. In this chapter, we present new semilocal and local convergence results for the Newton-Kantorovich method. These new results extend the appl...
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Article
Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation
We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is op...
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Article
On the election of the damped parameter of a two-step relaxed Newton-type method
In this paper, we are interested to justified two typical hypotheses that appear in the convergence analysis, \(|\lambda |\le 2\) ...
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Article
A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative
We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and ...
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Article
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 un...
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Article
A complex dynamical approach of Chebyshev’s method
The aim of this paper is to investigate the iterative root-finding Chebyshev’s method from a dynamical perspective. We analyze the behavior of the method applied to low degree polynomials. In this work we focu...
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Article
Improved local convergence analysis of the Gauss–Newton method under a majorant condition
We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97–...
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Article
Expanding the applicability of the Gauss–Newton method for convex optimization under a majorant condition
A new semi-local convergence analysis of the Gauss–Newton method for solving convex composite optimization problems is presented using the concept of quasi-regularity for an initial point. Our convergence anal...
