Numerical Algorithms

, Volume 72, Issue 2, pp 363–376 | Cite as

On the new family of optimal eighth order methods developed by Lotfi et al.

Original Paper
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Abstract

Recently Lotfi et al. (Numer. Algor. 68, 261–288, 5) have developed a new family of optimal order eight for the solution of nonlinear equations. They have experimented with 3 members of the family and compared them to other eighth order methods. One of the best known eight order method was not included. They also did not mention the best choice of parameters in the methods used and why. The basins of attraction were given for several examples without a quantitative comparison. It will be shown how to choose the best parameters in all these methods, and to quantitatively compare the methods.

Keywords

Iterative methods Order of convergence Basin of attraction Extraneous fixed points 

Mathematics Subject Classification (2010)

65H05 65B99 
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Copyright information

© Springer Science+Business Media New York (outside the USA) 2015

Authors and Affiliations

  1. 1.Department of MathematicsSungkyunkwan UniversitySuwonRepublic of Korea
  2. 2.Department of Applied MathematicsNaval Postgraduate SchoolMontereyUSA

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