On modified Newton–DGPMHSS method for solving nonlinear systems with complex symmetric Jacobian matrices

Abstract

This paper aims to give an efficient iterative method for solving large sparse nonlinear system with complex symmetric Jacobian matrix. Employing the double-parameter generalized preconditioned MHSS (DGPMHSS) method as the inner iteration, and using the modified Newton method as the outer iteration , we establish a modified Newton–DGPMHSS method for solving nonlinear system with complex symmetric Jacobian matrix. For the new presented method, we provide the local convergence analysis under Hölder condition, which is weaker than Lipschitz condition. Furthermore, we compare our new method with the modified Newton–PMHSS method, which is a considerable method for dealing with large sparse nonlinear system with complex symmetric Jacobian matrix, and the numerical results show the efficiency of our new method.