Scalable Parallel Preconditioning with the Sparse Approximate Inverse of Triangular Matrices

In this paper an approach is proposed for preconditioning large general sparse matrices. This approach combines the scalability of explicit preconditioners with the preconditioning eeciency of incomplete factorizations. Several algorithms resulting from this approach are presented. Both the preconditioning eeciency and the cost of applying this preconditioner are tested. The experiments indicate that this technique ooers the ability to make eecient use of parallel computers with a convergence rate comparable to that of the underlying incomplete factorization.