Augmented block splitting preconditioner for singular saddle point problems

In this paper, the augmented block splitting preconditioner is considered to solve singular saddle point problems. This preconditioner will result in a proper splitting for the saddle point matrix and the corresponding iteration method is proved to converge to the least squares solution of the singular saddle point problem. Besides, GMRES with this preconditioner will also converge to the least squares solution. Numerical experiments are presented to illustrate its effectiveness for solving singular saddle point problems.