Abstract:
This article discusses the iterative method by combining two Newton’s methods
where the second step of Newton’s method is given a weighted function. By pro-
viding specific requirements for this weighting function, it is shown using Taylor
expansion and geometric series that the iterative method have third and fourth or-
der of convergence. By choosing specific weighting functions, some known iterative
methods are found. Then some numerical simulations are performed to compare the
number of iterations of each discussed method