Null-Space Preconditioners for Saddle Point Systems

We will present theory that underpins the use of null-space preconditioners, giving eigenvalue bounds that show that the eigenvalues of the preconditioned system are clustered when a good approximation to the null-space matrix can be found. Additionally, we will describe how two of the family of preconditioners, although indefinite and non-symmetric, can be applied with a Krylov method with a short term recurrence.