Constructing higher-order methods for obtaining the multiple roots of nonlinear equations. (English) Zbl 1219.65048

Summary: 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.


65H05 Numerical computation of solutions to single equations
65Y20 Complexity and performance of numerical algorithms
68W30 Symbolic computation and algebraic computation
65Y15 Packaged methods for numerical algorithms


Full Text: DOI


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