Improving order and efficiency: Composition with a modified Newton's method (Q2271949)

The author presents a new zero-finding technique for solving nonlinear equations more efficiently in which the order of convergence is improved. The main idea is to compose a given iterative method with a modified Newton's method. The order of the convergence can be doubled while only one additional evaluation of the function is necessary. The result is a generalization of the Traub method [see Theorem 8--1 in \textit{J. F. Traub}, Iterative methods for the solution of equations. Englewood Cliffs: Prentice-Hall (1964; Zbl 0121.11204)]. The author considers three particular schemes obtained from well known iterative methods: Newton's, Chebyshev's and Schroeder's. To justify the superiority of the new technique, the results of numerical experiments are also presented and discussed.