A New Sixth Order Method for Nonlinear Equations in R

A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen x (0), the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton's method and other sixth order methods considered.