Robust cubically and quartically iterative techniques free from derivative

Constructing of a technique which is both accurate and derivativefree is one of the most important tasks in the field of iterative processes. Hence in this study, convergent iterative techniques are suggested for solving single variable nonlinear equations. Their error equations are given theoretica...

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Autores principales:	Soleymani,F, Hosseinabadi,V
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2011
Materias:	Derivative-free methods efficiency index error equation asymptotic error constant multi-point iterations optimal order
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200002
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spelling	oai:scielo:S0716-091720110002000022014-11-05Robust cubically and quartically iterative techniques free from derivativeSoleymani,FHosseinabadi,V Derivative-free methods efficiency index error equation asymptotic error constant multi-point iterations optimal order Constructing of a technique which is both accurate and derivativefree is one of the most important tasks in the field of iterative processes. Hence in this study, convergent iterative techniques are suggested for solving single variable nonlinear equations. Their error equations are given theoretically to show that they have cubic and quartical convergence. Per iteration the novel schemes include three evaluations of the function while they are free from derivative as well. In viewpoint of optimality, the developed quartically class reaches the optimal efficiency index 41/3 H" 1.587 based on the Kung-TraubHypothesis regarding the optimality of multi-point iterations without memory. In the end, the theoretical results are supported by numerical examples to elucidate the accuracy of the developed schemes.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.30 n.2 20112011-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200002en10.4067/S0716-09172011000200002
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Derivative-free methods efficiency index error equation asymptotic error constant multi-point iterations optimal order
spellingShingle	Derivative-free methods efficiency index error equation asymptotic error constant multi-point iterations optimal order Soleymani,F Hosseinabadi,V Robust cubically and quartically iterative techniques free from derivative
description	Constructing of a technique which is both accurate and derivativefree is one of the most important tasks in the field of iterative processes. Hence in this study, convergent iterative techniques are suggested for solving single variable nonlinear equations. Their error equations are given theoretically to show that they have cubic and quartical convergence. Per iteration the novel schemes include three evaluations of the function while they are free from derivative as well. In viewpoint of optimality, the developed quartically class reaches the optimal efficiency index 41/3 H" 1.587 based on the Kung-TraubHypothesis regarding the optimality of multi-point iterations without memory. In the end, the theoretical results are supported by numerical examples to elucidate the accuracy of the developed schemes.
author	Soleymani,F Hosseinabadi,V
author_facet	Soleymani,F Hosseinabadi,V
author_sort	Soleymani,F
title	Robust cubically and quartically iterative techniques free from derivative
title_short	Robust cubically and quartically iterative techniques free from derivative
title_full	Robust cubically and quartically iterative techniques free from derivative
title_fullStr	Robust cubically and quartically iterative techniques free from derivative
title_full_unstemmed	Robust cubically and quartically iterative techniques free from derivative
title_sort	robust cubically and quartically iterative techniques free from derivative
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2011
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200002
work_keys_str_mv	AT soleymanif robustcubicallyandquarticallyiterativetechniquesfreefromderivative AT hosseinabadiv robustcubicallyandquarticallyiterativetechniquesfreefromderivative
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Robust cubically and quartically iterative techniques free from derivative

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