Choosing the Forcing Terms in an Inexact Newton Method

摘要: An inexact Newton method is a generalization of Newton’s for solving $F(x) = 0,F:\mathbb{R}^n \to \mathbb{R}^n $in which, at the kth iteration, step $s_k $ from current approximate solution $x_k required to satisfy condition $\|F(x_k ) + F'(x_k )s_k \| \leqslant \eta _k \|F(x_k )\|$ “forcing term” $\eta \in [0,1)$. In typical applications, choice forcing terms critical efficiency and can affect robustness as well. Promising choices are given, their local convergence properties analyzed, practical performance shown on representative set test problems.