Robust semi-local convergence analysis for inexact Newton method

We present a more flexible semi-local convergence analysis for inexact Newton with relative residual error tolerance than in earlier studies. A combination of a majorant function and a center-majorant function is used in the convergence analysis. The center-majorant function is used instead of the majorant function to obtain more precise estimates. The advantages of the new approach are under the same computational cost: weaker convergence criteria; more precise error estimates on the distances involved and an at least as precise information on the location of the solution. Special cases and applications are also provided in the study.