Some modification of Newton’s method by the method of undetermined coefficients

In this paper, we construct some modifications of Newton’s method for solving nonlinear equations, which is based on the method of undetermined coefficients. It is shown by way of illustration that the method of undetermined coefficients is a promising tool for developing new methods, and reveals its wide applicability by obtaining some existing methods as special cases. Two new sixth-order methods are developed. Numerical examples are given to support that the methods thus obtained can compete with other iterative methods.