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On the Design of Optimal Iterative Methods for Solving Nonlinear Equations

  • Alicia Cordero
  • Juan R. TorregrosaEmail author
Chapter
Part of the SEMA SIMAI Springer Series book 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.

Notes

Acknowledgements

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

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Instituto de Matemáticas MultidisciplinarUniversidad Politécnica de ValenciaValenciaSpain

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