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Thresholds of the inner steps in multi-step Newton method. (English) Zbl 06916734
Summary: We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after $$m$$ steps) for solving nonlinear equations, $$F(x) = 0$$, $$F:D \subseteq R^n \rightarrow R^n$$. We highlight the following property of multi-step Newton method with respect to some other Newton-type method: for a given $$n$$, there exist thresholds of $$m$$, that is an interval $$(m_i, m_s)$$, such that for $$m$$ inside of this interval, the efficiency index of multi-step Newton method is better than that of other Newton-type method. We also search for optimal values of $$m$$.

##### MSC:
 65 Numerical analysis 35 Partial differential equations
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##### References:
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