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

Xiaojian Zhou
Xin Chen
Yongzhong Song
Journal / Anthology

Journal of Computational and Applied Mathematics
Year: 2011
Volume: 235
Issue: 14
Page range: 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 some known already. Numerical examples are also given to show their performance.