Displaying similar documents to “Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative”

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 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.

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.

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 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...