Modified Newton-SSTS method for solving a class of nonlinear systems with complex symmetric Jacobian matrices

This paper is intended to establish an effective iteration method for solving nonlinear systems with complex symmetric Jacobian matrices. Single-step triangular splitting (SSTS) iteration method is proved to be efficient and robust for solving a class of two-by-two block linear systems. By making use of the SSTS iteration scheme as the inner solver and the modified Newton method as the outer solver, we establish a new modified Newton-SSTS method to solve the class of nonlinear systems. Whereafter, we discuss the local and semilocal convergence properties of our method under the H o ¨ lder hypothesis. Finally, the numerical results of some nonlinear equations show that the Newton-SSTS method is vastly superior over some previous methods.