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Abstract and Applied Analysis
Volume 2014, Article ID 705674, 8 pages
Research Article

New Mono- and Biaccelerator Iterative Methods with Memory for Nonlinear Equations

1Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran
2Department of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, Iran
3Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Received 23 May 2014; Accepted 4 July 2014; Published 24 July 2014

Academic Editor: Alicia Cordero

Copyright © 2014 T. Lotfi et al. 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.


Acceleration of convergence is discussed for some families of iterative methods in order to solve scalar nonlinear equations. In fact, we construct mono- and biparametric methods with memory and study their orders. It is shown that the convergence orders 12 and 14 can be attained using only 4 functional evaluations, which provides high computational efficiency indices. Some illustrations will also be given to reverify the theoretical discussions.