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

journal contribution
posted on 2023-05-17, 22:28 authored by McDougall, TJ, Wotherspoon, SJ
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.

History

Publication title

Applied Mathematics Letters

Volume

29

Pagination

20-25

ISSN

0893-9659

Department/School

Institute for Marine and Antarctic Studies

Publisher

Pergamon-Elsevier Science Ltd

Place of publication

The Boulevard, Langford Lane, Kidlington, Oxford, England, Ox5 1Gb

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  • Restricted

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