  This paper presents a parallel preconditioning method for distributed sparse
linear systems, based on an approximate inverse of the original matrix, that
adopts a general framework of distributed sparse matrices and exploits the
domain decomposition method and low-rank corrections. The domain decomposition
approach decouples the matrix and once inverted, a low-rank approximation is
applied by exploiting the Sherman-Morrison-Woodbury formula, which yields two
variants of the preconditioning methods. The low-rank expansion is computed by
the Lanczos procedure with reorthogonalizations. Numerical experiments indicate
that, when combined with Krylov subspace accelerators, this preconditioner can
be efficient and robust for solving symmetric sparse linear systems.
Comparisons with other distributed-memory preconditioning methods are
presented.
