Numerical Algorithms

, Volume 61, Issue 4, pp 567–578

Modified Chebyshev-Halley type method and its variants for computing multiple roots

Original Paper

DOI: 10.1007/s11075-012-9551-4

Cite this article as:
Sharma, J.R. & Sharma, R. Numer Algor (2012) 61: 567. doi:10.1007/s11075-012-9551-4


We present two families of third order methods for finding multiple roots of nonlinear equations. One family is based on the Chebyshev-Halley scheme (for simple roots) and includes Halley, Chebyshev and Chun-Neta methods as particular cases for multiple roots. The second family is based on the variant of Chebyshev-Halley scheme and includes the methods of Dong, Homeier, Neta and Li et al. as particular cases. The efficacy is tested on a number of relevant numerical problems. It is observed that the new methods of the families are equally competitive with the well known special cases of the families.


Nonlinear equationsNewton methodChebyshev-Halley methodRootfindingMultiple rootsOrder of convergence

Mathematics Subject Classifications (2010)


Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsSant Longowal Institute of Engineering and TechnologyLongowalIndia
  2. 2.Department of Applied SciencesD.A.V. Institute of Engineering and TechnologyJalandharIndia