Krylov subspace methods for saddle point problems with indefinite preconditioning

In this paper we analyze the null-space projection (constraint) indefinite preconditioner applied to the solution of large-scale saddle point problems. Nonsymmetric Krylov subspace solvers are analyzed; moreover, it is shown that the behavior of short-term recurrence methods can be related to the behavior of preconditioned conjugate gradient method (PCG). Theoretical properties of PCG are studied in detail and simple procedures for correcting possible misconvergence are proposed. The numerical behavior of the scheme on a real application problem is discussed and the maximum attainable accuracy of the approximate solution computed in finite precision arithmetic is estimated.