Convergence of the modified SOR-Newton method for non-smooth equations

Motivated by Chen [On the convergence of SOR methods for nonsmooth equations. Numer. Linear Algebra Appl. 9 (2002), pp. 81-92], in this paper, we further investigate a modified SOR-Newton (MSOR-Newton) method for solving a system of nonlinear equations F(x)=0, where F is strongly monotone and locally Lipschitz continuous but not necessarily differentiable. The convergence interval of the parameter in the MSOR-Newton method is given. Compared with that of the SOR-Newton method, this interval can be enlarged. Furthermore, when the B-differential of F(x) is difficult to compute, a simple replacement can be used, which can reduce the computational load. Numerical examples show that at the same cost of computational complexity, this MSOR-Newton method can converge faster than the corresponding SOR-Newton method by choosing a suitable parameter.