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Calcolo

, Volume 53, Issue 2, pp 201–215 | Cite as

Solving nonlinear equations by a derivative-free form of the King’s family with memory

  • Somayeh SharifiEmail author
  • Stefan Siegmund
  • Mehdi Salimi
Article

Abstract

In this paper, we present an iterative three-point method with memory based on the family of King’s methods to solve nonlinear equations. This proposed method has eighth order convergence and costs only four function evaluations per iteration which supports the Kung-Traub conjecture on the optimal order of convergence. An acceleration of the convergence speed is achieved by an appropriate variation of a free parameter in each step. This self accelerator parameter is estimated using Newton’s interpolation polynomial of fourth degree. The order of convergence is increased from 8 to 12 without any extra function evaluation. Consequently, this method, possesses a high computational efficiency. Finally, a numerical comparison of the proposed method with related methods shows its effectiveness and performance in high precision computations.

Keywords

Multi-point method Nonlinear equations Method with memory R-order of convergence Kung-Traub’s conjecture 

Mathematics Subject Classification

65H05 

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Copyright information

© Springer-Verlag Italia 2015

Authors and Affiliations

  • Somayeh Sharifi
    • 1
    Email author
  • Stefan Siegmund
    • 2
  • Mehdi Salimi
    • 2
  1. 1.Young Researchers and Elite Club, Hamedan BranchIslamic Azad UniversityHamedanIran
  2. 2.Center for Dynamics, Department of MathematicsTechnische Universität DresdenDresdenGermany

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