Thresholds of the Inner Steps in Multi-Step Newton Method
Department of Informatics, West University of Timisoara, B-dul V. Parvan No.4, Timisoara 300223, Romania
Received: 2 June 2017 / Revised: 23 June 2017 / Accepted: 24 June 2017 / Published: 27 June 2017
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,
. 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
, 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
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Maruster, S. Thresholds of the Inner Steps in Multi-Step Newton Method. Algorithms 2017, 10, 75.
Maruster S. Thresholds of the Inner Steps in Multi-Step Newton Method. Algorithms. 2017; 10(3):75.
Maruster, Stefan. 2017. "Thresholds of the Inner Steps in Multi-Step Newton Method." Algorithms 10, no. 3: 75.
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