Abstract
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.
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Sharma, J.R., Sharma, R. Modified Chebyshev-Halley type method and its variants for computing multiple roots. Numer Algor 61, 567–578 (2012). https://doi.org/10.1007/s11075-012-9551-4
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DOI: https://doi.org/10.1007/s11075-012-9551-4
Keywords
- Nonlinear equations
- Newton method
- Chebyshev-Halley method
- Rootfinding
- Multiple roots
- Order of convergence