Constraint preconditioning for indefinite linear systems

The problem of finding good preconditioners for the numerical solution of i ndefinite linear systems is considered. Special emphasis is put on precondi tioners that have a 2 x 2 block structure and that incorporate the (1, 2) a nd (2, 1) blocks of the original matrix. Results concerning the spectrum an d form of the eigenvectors of the preconditioned matrix and its minimum pol ynomial are given. The consequences of these results are considered for a v ariety of Krylov subspace methods. Numerical experiments validate these con clusions.