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Advances in Iterative Methods for Nonlinear Equations pp 79–111Cite as

On the Design of Optimal Iterative Methods for Solving Nonlinear Equations

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Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 10))

Abstract

A survey on the existing techniques used to design optimal iterative schemes for solving nonlinear equations is presented. The attention is focused on such procedures that use some evaluations of the derivative of the nonlinear function. After introducing some elementary concepts, the methods are classified depending on the optimal order reached and also some general families of arbitrary order are presented. Later on, some techniques of complex dynamics are introduced, as this is a resource recently used for many authors in order to classify and compare iterative methods of the same order of convergence. Finally, some numerical test are made to show the performance of several mentioned procedures and some conclusions are stated.

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Acknowledgements

This scientific work has been supported by Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P.

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  1. Instituto de Matemáticas Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera, s/n 46022, Valencia, Spain

    Alicia Cordero & Juan R. Torregrosa

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  1. Alicia Cordero
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  2. Juan R. Torregrosa
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Correspondence to Juan R. Torregrosa .

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  1. Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

    Sergio Amat

  2. Departamento de Matemática, Aplicada y Estadística Universidad Politécnica de Cartagena, Cartagena, Spain

    Sonia Busquier

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Cordero, A., Torregrosa, J.R. (2016). On the Design of Optimal Iterative Methods for Solving Nonlinear Equations. In: Amat, S., Busquier, S. (eds) Advances in Iterative Methods for Nonlinear Equations. SEMA SIMAI Springer Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-39228-8_5

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