Ideal Preconditioners for Saddle Point Systems with a Rank-Deficient Leading Block
Provides ideal preconditioners for solving saddle point systems with rank-deficient leading blocks, a known bottleneck in numerical linear algebra.
Developed preconditioners for symmetric saddle point systems with rank-deficient leading blocks that achieve a constant number of eigenvalues in the preconditioned matrix, with one preconditioner remaining ideal under relaxed rank assumptions.
We consider the iterative solution of symmetric saddle point systems with a rank-deficient leading block. We develop two preconditioners that, under certain assumptions on the rank structure of the system, yield a preconditioned matrix with a constant number of eigenvalues. We then derive some properties of the inverse of a particular class of saddle point system and exploit these to develop a third preconditioner, which remains ideal even when the earlier assumptions on rank structure are relaxed.