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A simple modification of Newton's method to achieve convergence of order 1 + √2
Citation
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]
Copyright Statement
Copyright
DOI: doi:10.1016/j.aml.2013.10.008
Abstract
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: | 30 |
| Deposited By: | IMAS Research and Education Centre |
| Deposited On: | 2014-02-24 |
| Last Modified: | 2017-10-30 |
| Downloads: | 0 |
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