Abstract:
We discuss a derivation of a high-order iterative method based on Taylor expansion
of a nonlinear function. The method is a special case of the method derived by
Germani, A., et al. in Journal of Optimization Theory and Applications. 131 (2006). 347-364. We show analytically with a different technique from those of Germani that the method is of four order. The numerical simulation using four nonlinear functions shows that the performance of the method is better than those of Newton method,
Traub method, Halley method, and Chebyshev method.
