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 Type:	Refereed Article
Keywords:	Newton's method, nonlinear equations
Research Division:	Earth Sciences
Research Group:	Oceanography
Research Field:	Physical Oceanography
Objective Division:	Environment
Objective Group:	Climate and 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:	23
Deposited By:	IMAS Research and Education Centre
Deposited On:	2014-02-24
Last Modified:	2017-10-30
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