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On two high-order families of frozen Newton-type methods. (English) Zbl 1424.65072

This paper considers a two-step method to approximate the solution of a nonlinear equation that increases the order of Newton-type methods but without evaluating any second Fréchet derivative. The results are generalized to new families of iterative methods. The semilocal convergence analysis using weaker conditions is established. Some numerical examples are presented.

MSC:

65J15 Numerical solutions to equations with nonlinear operators

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