  To precondition a large and sparse linear system, two direct methods for
approximate factoring of the inverse are devised. The algorithms are fully
parallelizable and appear to be more robust than the iterative methods
suggested for the task. A method to compute one of the matrix subspaces
optimally is derived. Possessing a considerable amount of flexibility, these
approaches extend the approximate inverse preconditioning techniques in several
natural ways. Numerical experiments are given to illustrate the performance of
the preconditioners on a number of challenging benchmark linear systems.
