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

作者：Chun Changbum

来源：Journal of Computational and Applied Mathematics, 2008, 219(1): 81-89.

DOI：10.1016/j.cam.2007.07.004

• Newton's method
• iterative methods
• nonlinear equations
• order of convergence
• Chebyshev-Halley methods
• root-finding methods

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.

• 出版日期2008-9-15