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Algorithms 2016, 9(1), 14; doi:10.3390/a9010014

Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems

School of Mathematics and Physics, Bohai University, Jinzhou 121013, China
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Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Received: 16 October 2015 / Revised: 26 January 2016 / Accepted: 27 January 2016 / Published: 1 February 2016
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
View Full-Text   |   Download PDF [277 KB, uploaded 1 February 2016]   |  

Abstract

In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Numerical experiments support the theoretical results. Experimental results show that the new methods remarkably reduce the computing time in the process of high-precision computing. View Full-Text
Keywords: system of nonlinear equations; derivative-free iterative methods; order of convergence; high precision system of nonlinear equations; derivative-free iterative methods; order of convergence; high precision
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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. (CC BY 4.0).

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Wang, X.; Fan, X. Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems. Algorithms 2016, 9, 14.

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