The Parameterized Augmentation Block Preconditioner for Nonsymmetric Saddle Point Problems

Based on the preconditioner presented by He and Huang (Comput Math Appl 62: 87–92, 2011), we introduce a parameterized augmentation block preconditioner for solving the nonsymmetric saddle point problems with the singular (1,1)-block. The theoretical analysis gives the eigenvalue and eigenvector properties of the corresponding preconditioned matrix, and numerical results confirm the effectiveness of the preconditioner for accelerating the convergence rate of the generalized minimal residual (GMRES) method when solving the large sparse nonsymmetric saddle point problems.