On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations

The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub's co...

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Detalles Bibliográficos
Autores principales: Lotfi, Taher, Cordero, Alicia, Torregrosa, Juan R., Amir Abadi, Morteza, Mohammadi Zadeh, Maryam
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3916023/
https://www.ncbi.nlm.nih.gov/pubmed/24563629
http://dx.doi.org/10.1155/2014/272949
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author Lotfi, Taher
Cordero, Alicia
Torregrosa, Juan R.
Amir Abadi, Morteza
Mohammadi Zadeh, Maryam
author_facet Lotfi, Taher
Cordero, Alicia
Torregrosa, Juan R.
Amir Abadi, Morteza
Mohammadi Zadeh, Maryam
author_sort Lotfi, Taher
collection PubMed
description The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub's conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of this class are shown and implemented numerically, showing their applicability and efficiency.
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spelling pubmed-39160232014-02-23 On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations Lotfi, Taher Cordero, Alicia Torregrosa, Juan R. Amir Abadi, Morteza Mohammadi Zadeh, Maryam ScientificWorldJournal Research Article The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub's conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of this class are shown and implemented numerically, showing their applicability and efficiency. Hindawi Publishing Corporation 2014-01-19 /pmc/articles/PMC3916023/ /pubmed/24563629 http://dx.doi.org/10.1155/2014/272949 Text en Copyright © 2014 Taher Lotfi et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Lotfi, Taher
Cordero, Alicia
Torregrosa, Juan R.
Amir Abadi, Morteza
Mohammadi Zadeh, Maryam
On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
title On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
title_full On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
title_fullStr On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
title_full_unstemmed On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
title_short On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
title_sort on generalization based on bi et al. iterative methods with eighth-order convergence for solving nonlinear equations
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3916023/
https://www.ncbi.nlm.nih.gov/pubmed/24563629
http://dx.doi.org/10.1155/2014/272949
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