Some quadrature-based versions of the generalized Newton method for solving nonsmooth equations

In this paper, modifications of a generalized Newton method based on some rules of quadrature are studied. The methods considered are Newton-like iterative schemes for numerical solving systems of nonsmooth equations. Some mild conditions are given that ensure superlinear convergence to a solution. Moreover, a parameterized version of the midpoint version is presented. Finally, results of numerical tests are established.