Title: Choosing the forcing terms in an inexact Newton method 

Authors: Stanley C. Eisenstat and Homer F. Walker 

Abstract: An inexact Newton method is a generalization of Newton's 
method for solving a nonlinear system in which, at the each iteration, 
the step from the current approximate solution is required to reduce 
the norm of the local linear model. The amount by which the local 
linear model norm is reduced is specified by a ``forcing term''. 
In typical applications, the choice of the forcing terms is critical 
to the efficiency of the method and can affect robustness as well. 
Promising choices of the forcing terms are given, their local convergence 
properties are analyzed, and their practical performance is shown on 
a representative set of test problems.