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New families of nonlinear third-order solvers for finding multiple roots. (English) Zbl 1186.65060
Summary: We present two new families of iterative methods for multiple roots of nonlinear equations. One of the families require one-function and two-derivative evaluation per step, and the other family requires two-function and one-derivative evaluation. It is shown that both are third-order convergent for multiple roots. Numerical examples suggest that each family member can be competitive to other third-order methods and Newton’s method for multiple roots. In fact the second family is even better than the first.

MSC:
65H05 Numerical computation of solutions to single equations
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