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.
Keywords
- Optimal Eighth-order
- Optimal Fourth-order Methods
- Kung-Traub Conjecture
- Iterative Expression
- Chebyshev Halley Methods
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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This scientific work has been supported by Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P.
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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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