An augmentation preconditioner for a class of complex symmetric linear systems

In this paper, we propose an efficient augmentation-based preconditioner for solving complex symmetric linear systems, which is obtained by augmenting the (2,2) block of the coefficient matrix. Then, the convergence of the corresponding iteration method is analyzed, and several spectral properties of the preconditioned matrices, such as eigenvalue distributions and eigenvectors, are also discussed. Numerical experiments demonstrate that our proposed preconditioner is more effective than some existing block preconditioners.