A Technique to Composite a Modified Newton's Method for Solving   Nonlinear Equations
  A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to compose a given iterative method with a modified Newton's method that introduces just one evaluation of the function. To carry out this procedure some classical methods with different orders of convergence are used to obtain root-finders with higher efficiency index. 
Miquel Grau-S\'anchez and Jos\'e Luis D\'iaz-Barrero
math.NA