Forcing sequences and inexact Newton iterates in Banach space
This paper deals with inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Under an assumption on the second Fréchet-derivative of the operator involved, the author essentially reproduces all results found earlier. In particular, the author shows inexact Newton methods are locally convergent if the forcing sequence is uniformly less than one and shows how to choose a forcing sequence which preserves the rapid convergence of Newton's method. However, the obtained upper error bounds on the distances involved are smaller.
scientific article; zbMATH DE number 1429493