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A simply constructed third-order modifications of Newton's method

✍ Scribed by Changbum Chun

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
145 KB
Volume
219
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper, we present a simple and easily applicable approach to construct some third-order modifications of Newton's method for solving nonlinear equations. It is shown by way of illustration that existing third-order methods can be employed to construct new third-order iterative methods. The proposed approach is applied to the classical Chebyshev-Halley methods to derive their second-derivative-free variants. Numerical examples are given to support that the methods thus obtained can compete with known third-order methods.

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