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A simple modification of Newton's method to achieve convergence of order 1 + √2


McDougall, TJ and Wotherspoon, SJ, A simple modification of Newton's method to achieve convergence of order 1 + √2, Applied Mathematics Letters, 29 pp. 20-25. ISSN 0893-9659 (2014) [Refereed Article]

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DOI: doi:10.1016/j.aml.2013.10.008


A simple modification to the standard Newton method for approximating the root of a uni- variate function is described and analyzed. For the same number of function and deriva- tive evaluations, the modified method converges faster, with the convergence order of the method being 1 +√ 2 ≈ 2.4 compared with 2 for the standard Newton method. Numerical examples demonstrate the faster convergence achieved with this modification of Newton’s method. This modified Newton–Raphson method is relatively simple and is robust; it is more likely to converge to a solution than are either the higher order (4th order and 6th order) schemes or Newton’s method itself.

Item Details

Item Type:Refereed Article
Keywords:Newton's method, nonlinear equations
Research Division:Earth Sciences
Research Group:Oceanography
Research Field:Physical oceanography
Objective Division:Environmental Policy, Climate Change and Natural Hazards
Objective Group:Understanding climate change
Objective Field:Climate change models
UTAS Author:Wotherspoon, SJ (Dr Simon Wotherspoon)
ID Code:89069
Year Published:2014
Web of Science® Times Cited:35
Deposited By:IMAS Research and Education Centre
Deposited On:2014-02-24
Last Modified:2017-10-30

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