1996/01/01 by Stanley C. Eisenstat, Homer F. Walker · 12 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms
paper · doi:10.1137/0917003
openalex publication_date 1996/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
An inexact Newton method is a generalization of Newton’s method for solving F(x) = 0,F:ℝn → ℝn in which, at the kth iteration, the step sk from the current approximate solution xk is required to satisfy a condition ‖F(xk ) + F'(xk )sk ‖ \leqslant η k ‖F(xk )‖ for a “forcing term” η k ∈ [0,1). 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.