Modified Newton-PSBTS method for solving complex nonlinear systems with symmetric Jacobian matrices

Abstract

The main purpose of this paper is to give an effective iterative method for solving complex nonlinear systems with symmetric Jacobian matrices called the modified Newton preconditioned symmetric block triangular splitting (MN-PSBTS) iteration method. In order to obtain the solution of complex nonlinear systems with symmetric Jacobian matrix, by employing the preconditioned symmetric block triangular splitting (PSBTS) method as the inner iteration to solve Newton equations, we establish the modified Newton-PSBTS method. For the new presented method, we give the local convergence analysis and give the proof under appropriate conditions. Furthermore, we compare MN-PSBTS method with some other methods proposed recently, and the numerical results show the efficiency and superiority of our new method. Especially, in terms of CPU time and iteration steps our method is obviously better.