On preconditioned modified Newton-MHSS method for systems of nonlinear equations with complex symmetric jacobian matrices

Preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) method is an unconditionally convergent iterative method for solving large sparse complex symmetric systems of linear equations. By making use of the PMHSS iteration as the inner solver to approximately solve the Newton equations, we establish a modified Newton-PMHSS method for solving large systems of nonlinear equations. Motivated by the idea in Chen et al. (2014), we analyze the local convergence properties under the Hölder continuous condition, which is weaker than the assumptions used in modified Newton-HSS method proposed by Wu and Chen (2013). Numerical results are given to confirm the effectiveness of our method.