Extending the applicability of the inexact Newton-HSS method for solving large systems of nonlinear equations

Abstract

We revisit the study of the semi-local convergence of the inexact Newton-HSS method (INHSS) introduced by Amiri et al. (2018), for solving large systems of nonlinear equations. In particular, first we present the correct convergence criterion, since the one in the preceding reference is incorrect. Secondly, we present an even weaker convergence criterion using our idea of recurrent functions. Moreover, the bound functions are compared. Finally, numerical examples are provided to show that the earlier convergence criteria are not satisfied but the new ones are satisfied. Hence, the applicability of the INHSS method is extended and under the same information as in the earlier studies.