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SeMA Journal

, Volume 74, Issue 4, pp 361–369 | Cite as

Computing multiple zeros by using a parameter in Newton–Secant method

  • Massimiliano Ferrara
  • Somayeh Sharifi
  • Mehdi SalimiEmail author
Article

Abstract

In this paper, we modify the Newton–Secant method with third order of convergence for finding multiple roots of nonlinear equations. This method requires two evaluations of the function and one evaluation of its first derivative per iteration. This method has the efficiency index equal to \(3^{\frac{1}{3}}\approx 1.44225\). We describe the analysis of the proposed method along with numerical experiments including comparison with existing methods. Moreover, the attraction basins of the proposed method are shown and compared with other existing methods.

Keywords

Multi-point iterative methods Newton–Secant method  Multiple roots Basin of attraction 

Mathematics Subject Classification

65H05 

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Copyright information

© Sociedad Española de Matemática Aplicada 2016

Authors and Affiliations

  1. 1.Department of Law and EconomicsUniversity Mediterranea of Reggio CalabriaReggio CalabriaItaly
  2. 2.MEDAlics, Research Centre at the University Dante AlighieriReggio CalabriaItaly
  3. 3.Center for Dynamics, Department of MathematicsTechnische Universität DresdenDresdenGermany

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