A multidimensional generalization of some classes of free-derivative iterative methods to solve nonlinear equations

A multidimensional generalization of some classes of free-derivative iterative methods to solve... In this paper we extend to the multidimensional case six free-derivative iterative methods that are known in their scalar version. In order to construct new multidimensional iterative algorithms we develop a new idea based on two operators. All the schemes considered here are two-step methods in which the first step is Steffensen’s method and they have fourth-order local convergence, depending on the function. We analyze the efficiency of these six new algorithms and conclude which ones are the most efficient. We illustrate these results with some numerical examples, where their order of convergence is discussed. Finally, a study comparing the efficiency and elapsed time of the suggested methods supports the claimed theoretical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

A multidimensional generalization of some classes of free-derivative iterative methods to solve nonlinear equations

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Publisher
Springer Milan
Copyright
Copyright © 2016 by Sociedad Española de Matemática Aplicada
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0100-2
Publisher site
See Article on Publisher Site

Abstract

In this paper we extend to the multidimensional case six free-derivative iterative methods that are known in their scalar version. In order to construct new multidimensional iterative algorithms we develop a new idea based on two operators. All the schemes considered here are two-step methods in which the first step is Steffensen’s method and they have fourth-order local convergence, depending on the function. We analyze the efficiency of these six new algorithms and conclude which ones are the most efficient. We illustrate these results with some numerical examples, where their order of convergence is discussed. Finally, a study comparing the efficiency and elapsed time of the suggested methods supports the claimed theoretical results.

Journal

SeMA JournalSpringer Journals

Published: Nov 18, 2016

References

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