Modified Newton-MDPMHSS method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices

In this study, an efficient iterative method is given to solve large sparse nonlinear systems with block two-by-two complex symmetric Jacobian matrices. Based on the double-parameter preconditioned MHSS (DPMHSS) method, a modified double-parameter preconditioned MHSS (MDPMHSS) method is developed to solve a class of linear systems with block two-by-two complex coefficient matrices. Then, a modified Newton-MDPMHSS method for solving nonlinear systems with block two-by-two complex symmetric Jacobian matrices is obtained, which MDPMHSS is employed as the inner iteration and the modified Newton method is employed as the outer iteration. Local convergence analysis is given for the new present method under Holder condition, which is weaker than Lipschitz condition. At last, numerical results are reported to verify the efficiency of the new method.