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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.20 no.3 Temuco oct. 2018

http://dx.doi.org/10.4067/S0719-06462018000300065 

Articles

Ball comparison between Jarratt’s and other fourth order method for solving equations

Ioannis K. Argyros1 

Santhosh George2 

1Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA. iargyros@cameron.edu.

2National Institute of Technology Karnataka, Department of Mathematical and Computational Sciences, India-575 025. sgeorge@nitk.edu.in

Abstract

The convergence order of iterative methods is determined using high order derivatives and Taylor series, and without providing computable error bounds, uniqueness of the solution results or information on how to choose the initial point. We address all these problems by using hypotheses only on the first derivative. Moreover, to achieve all these we present our technique using a comparison between the convergence radii of Jarratt’s fourth order method and another method of the same convergence order.

Keywords and Phrases: Jarratt method; Banach space; Ball convergence

Resumen

El orden de convergencia de métodos iterativos es determinado usando derivadas de orden alto y series de Taylor, y sin poder entregar cotas de error calculables, resultados de unicidad de soluciones o información de cómo elegir el punto inicial. Tratamos estos problemas usando hipótesis sólo en la primera derivada. Más aún, para responder todos los anteriores, presentamos una técnica que usa una comparación entre el radio de convergencia del método de cuarto orden de Jarratt y otro método con el mismo orden de convergencia.

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