Numerical Analysis and Applications

, Volume 9, Issue 2, pp 129–140 | Cite as

Optimized mean based second derivative-free families of Chebyshev–Halley type methods

  • M. Kansal
  • V. Kanwar
  • S. Bhatia


In this paper, we present new interesting fourth-order optimal families of Chebyshev–Halley type methods free from second-order derivative. In terms of computational cost, eachmember of the families requires two functions and one first-order derivative evaluation per iteration, so that their efficiency indices are 1.587. It is found by way of illustration that the proposed methods are useful in high-precision computing environment. Moreover, it is also observed that larger basins of attraction belong to ourmethods although the othersmethods are slow and have darker basins while some of the methods are too sensitive upon the choice of the initial guess.


basins of attraction Newton’smethod King’smethods optimal iterativemethods efficiency index 


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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.University Institute of Engineering and TechnologyPanjab UniversityChandigarhIndia

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