Scientific Computation and Applied & Industrial Mathematics Seminar: Chen Greif

We consider nonsingular saddle-point matrices whose (1,1) block is maximally rank deficient, and show that the inverse in this case has unique mathematical properties. We then develop a class of indefinite block preconditioners that rely on approximating the null space of the leading block. Under certain conditions, even though the preconditioned matrix is a product of two indefinite matrices, the conjugate gradient method can be applied and is rapidly convergent. Spectral properties of the preconditioners are observed, which are validated by numerical experiments.

This is joint work with Ron Estrin.