A variant of Chebyshev’s method with sixth-order convergence

@article{Kou2006AVO,
  title={A variant of Chebyshev’s method with sixth-order convergence},
  author={Jisheng Kou and Yitian Li},
  journal={Numerical Algorithms},
  year={2006},
  volume={43},
  pages={273-278}
}
In this paper, we present a new variant of Chebyshev’s method for solving non-linear equations. Analysis of convergence shows that the new method has sixth-order convergence. Per iteration the new method requires two evaluations of the function, one of its first derivative and one of its second derivative. Thus the efficiency, in term of function evaluations, of the new method is better than that of Chebyshev’s method. Numerical examples verifying the theory are given.