A general class of constraint preconditioners for generalized saddle point linear systems

We propose a general class of constraint preconditioners for solving generalized saddle point linear systems, derived from a general matrix splitting of the (1,1) block of the coefficient matrix. This new constraint preconditioner can not only reduce to some existing constraint preconditioners, but also induce new constraint preconditioners under some certain matrix splitting schemes. Then we present invertibility conditions of the proposed constraint preconditioner and establish the convergence analysis of the corresponding constraint preconditioning iteration method. Numerical examples are provided to confirm that the proposed preconditioner outperforms existing ones when suitable matrix splitting schemes are chosen.