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Zbl 1122.65332
Kou, Jisheng
The improvements of modified Newton's method. (English)
[J] Appl. Math. Comput. 189, No. 1, 602-609 (2007). ISSN 0096-3003

Summary: We improve some third-order modifications of Newton's method and obtain many new methods for solving non-linear equations. The new methods have the order of convergence five or six. Per iteration these methods require two evaluations of the function and two evaluations of its first derivative and therefore the efficiency of the new methods may also be improved. These methods can compete with Newton's method, as we show in some examples.

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)

Keywords: Newton's method; non-linear equations; root-finding; iterative method; numerical example; convergence

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Zentralblatt MATH Berlin [Germany]