Displaying similar documents to “Local-global convergence, an analytic and structural approach”

Local convergence comparison between two novel sixth order methods for solving equations

Santhosh George, Ioannis K. Argyros (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples...

Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative

Ioannis K. Argyros, Santhosh George (2017)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator...

On an iterative method for unconstrained optimization

Ioannis K. Argyros (2015)

Applicationes Mathematicae

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We present a local and a semi-local convergence analysis of an iterative method for approximating zeros of derivatives for solving univariate and unconstrained optimization problems. In the local case, the radius of convergence is obtained, whereas in the semi-local case, sufficient convergence criteria are presented. Numerical examples are also provided.

Local convergence of two competing third order methods in Banach space

Ioannis K. Argyros, Santhosh George (2014)

Applicationes Mathematicae

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We present a local convergence analysis for two popular third order methods of approximating a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for both methods under the same conditions. A comparison is given between the two methods, as well as numerical examples.

Local convergence for a family of iterative methods based on decomposition techniques

Ioannis K. Argyros, Santhosh George, Shobha Monnanda Erappa (2016)

Applicationes Mathematicae

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We present a local convergence analysis for a family of iterative methods obtained by using decomposition techniques. The convergence of these methods was shown before using hypotheses on up to the seventh derivative although only the first derivative appears in these methods. In the present study we expand the applicability of these methods by showing convergence using only the first derivative. Moreover we present a radius of convergence and computable error bounds based only on Lipschitz...

On the local convergence of Kung-Traub's two-point method and its dynamics

Parandoosh Ataei Delshad, Taher Lotfi (2020)

Applications of Mathematics

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In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by...

On the exponential local-global principle

Boris Bartolome, Yuri Bilu, Florian Luca (2013)

Acta Arithmetica

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Skolem conjectured that the "power sum" A(n) = λ₁α₁ⁿ + ⋯ + λₘαₘⁿ satisfies a certain local-global principle. We prove this conjecture in the case when the multiplicative group generated by α₁,...,αₘ is of rank 1.