Concerning the convergence of inexact Newton methods
An inexact Newton method of the form \[ x_{n+1}=x_n+F'(x_n)^{*}[-F(x_n)+Q(x_n))]-z_n,\quad z_0=0\;(n\geq 0) \] is considered to approximate the solution \(x^{*}\) of a nonlinear operator equation of the form \[ F(x)+Q(x)=0, \] where \(Q\) is a nondifferentiable and \(F\) is a differentiable operator. The usefulness of this method is also illustrated by applying it to solve problems that cannot be solved with existing methods.
scientific article; zbMATH DE number 1022221