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

Abstract

We present the semilocal convergence of a modified Newton-HSS method to approximate a solution of a nonlinear equation. Earlier studies show convergence under only Lipschitz conditions limiting the applicability of this method. The convergence in this study is shown under generalized Lipschitz-type conditions and restricted convergence domains. Hence, the applicability of the method is expanded. Moreover, numerical examples are also provided to
show that our results can be applied to solve equations in cases where earlier study cannot be applied. Furthermore, in the cases where both old and new results are applicable, the latter provides a larger domain of convergence and tighter error bounds on the distances involved.