Improved local convergence analysis of inexact Gauss–Newton like methods under the majorant condition in Banach spaces

We present a local convergence analysis of inexact Gauss–Newton like methods for solving nonlinear equations in a Banach space setting. Using more precise majorant conditions than in earlier studies, we provide a larger radius of convergence; tighter error estimates on the distances involved and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.