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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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