CHOOSING THE FORCING TERMS IN AN INEXACT NEWTON METHOD

An inexact Newton method is a generalization of Newton's method for so lving F(x)=0, F:R(n) right arrow R(n), in which, at the kth iteration, the step s(k) from the current approximate solution x(k) is required to satisfy a condition parallel to F(x(k))+F'(x(k))s(k) parallel to le ss than or equal to eta(k) parallel to F(x(k)) parallel to for a ''for cing term'' eta(k) is an element of [0,1]. In typical applications, th e choice of the forcing terms is critical to the efficiency of the met hod and can affect robustness as well. Promising choices of the forcin g terms are given, their local convergence properties are analyzed, an d their practical performance is shown on a representative set of test problems.