Newton-PGSS and Its Improvement Method for Solving Nonlinear Systems with Saddle Point Jacobian Matrices

The preconditioned generalized shift-splitting (PGSS) iteration method is unconditionally convergent for solving saddle point problems with nonsymmetric coefficient matrices. By making use of the PGSS as inner solver Newton method, we establish a class Newton-PGSS large sparse nonlinear system Jacobian matrices about problems. For new presented give local convergence analysis and semilocal under Hölder condition, which weaker than Lipschitz condition. In order to further raise efficiency algorithm, improve obtain modified prove its convergence. Furthermore, compare our methods Newton-RHSS considerable matrix, numerical results show method.