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Algorithms 2017, 10(3), 75; doi:10.3390/a10030075

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
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Abstract

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 R n 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. View Full-Text
Keywords: multi-step Newton method; efficiency index; threshold of inner steps multi-step Newton method; efficiency index; threshold of inner steps
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Maruster, S. Thresholds of the Inner Steps in Multi-Step Newton Method. Algorithms 2017, 10, 75.

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