Displaying similar documents to “Relaxing convergence conditions for the Jarratt method.”

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 multi-point family of super-Halley methods in a Banach space under weak conditions

Ioannis K. Argyros, Santhosh George (2015)

Applicationes Mathematicae

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We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.

On the convergence and application of Stirling's method

Ioannis K. Argyros (2003)

Applicationes Mathematicae

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We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones. ...

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...

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...

Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions

Ioannis K. Argyros, Saïd Hilout (2011)

Applicationes Mathematicae

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We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.