Newton-like iteration methods for solving non-linear equations

摘要

In this paper, Newton-like iteration methods for solving non-linear equations or improving the existing iteration methods are proposed. The iteration formulae are obtained by applying the homotopy perturbation method which contains the well-known Newton iteration formula in logic, so those improving the Newton method. The orders of convergence of some of those iteration formulae are derived analytically and by applying symbolic computation of Maple. Some numerical illustrations are given.