A two-step SOR-Newton method for nonsmooth equations

In this paper, we present a two-step SOR-Newton method for solving a system of nonlinear equations F(x)=0F(x)=0, where FF is strongly monotone, locally Lipschitz continuous but not necessarily differentiable. The convergence of the two-step SOR-Newton method is discussed. For any starting point, we give safe intervals such that for any parameters in these intervals the two-step SOR-Newton method converges. Numerical examples show that the two-step SOR-Newton method converges faster than the SOR-Newton method given by Chen in [X. Chen, On convergence of SOR methods for nonsmooth equations, Numer. Linear Algebra Appl. 9 (2002) 81–92].