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On some modified families of multipoint iterative methods for multiple roots of nonlinear equations. (English) Zbl 1251.65069
Authors’ abstract: A new one-parameter family of Schröder’s method is proposed for finding the multiple roots of nonlinear equations numerically. Further, many new cubically convergent families of Schröder-type methods are derived. The proposed families are derived from the modified Newton’s method for multiple roots and from a one-parameter family of Schröder’s methods. Furthermore, new families of third-order multipoint iterative methods for multiple roots free from second-order derivative by semidiscrete modifications of the above proposed methods are introduced. One of the families requires two evaluations of the function and one evaluation of its first-order derivative and the other family requires one evaluation of the function and two evaluations of its first-order derivative per iteration. Numerical examples are also presented to demonstrate the performance of propsed iterative methods.

MSC:
65H05 Numerical computation of solutions to single equations
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