Constructing higher-order methods for obtaining the multiple roots of nonlinear equations

@article{Zhou2011ConstructingHM,
  title={Constructing higher-order methods for obtaining the multiple roots of nonlinear equations},
  author={Xiaojian Zhou and Xin Chen and Yongzhong Song},
  journal={J. Computational Applied Mathematics},
  year={2011},
  volume={235},
  pages={4199-4206}
}
This paper concentrates on iterative methods for obtaining the multiple roots of nonlinear equations. Using the computer algebra system Mathematica, we construct an iterative scheme and discuss the conditions to obtain fourth-order methods from it. All the presented fourth-order methods require one-function and two-derivative evaluation per iteration, and are optimal higher-order iterative methods for obtaining multiple roots. We present some special methods from the iterative scheme, including… CONTINUE READING

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