Inexact splitting-based block preconditioners for block two-by-two linear systems

Based on the splitting-based block preconditioners presented by Yan and Huang (2014), a class of inexact splitting-based block preconditioners are constructed. Then, computing exactly inversion of the matrix αW+TαW+T can be avoided for solving the linear subsystem during the preconditioning process. Spectral properties of the preconditioned matrices are investigated. Some numerical examples are provided to illustrate the effectiveness of the proposed preconditioners, in comparison with corresponding exact versions and inexact rotated block triangular preconditioners.