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A cubically convergent Newton-type method under weak conditions

✍ Scribed by Liang Fang; Guoping He; Zhongyong Hu

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
119 KB
Volume
220
Category
Article
ISSN
0377-0427

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✦ Synopsis

Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f (x) = 0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative. Analysis of convergence demonstrates that the new method is cubically convergent. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newton's method.

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