Substructure preconditioners for a class of structured linear systems of equations

We proposed a substructure preconditioner for a class of structured linear system of equations. We show that a preconditioner with half of the constraint terms is able to make the preconditioned matrix have only three distinct eigenvalues. For some practical applications, a regularized variant is formulated, and the influence of the regularization parameter is analyzed. Numerical results show that the regularized variant is as efficient and is able to produce nearly optimal convergence behavior with a wide range of parameters.