We make a detailed examination lwas made of the performance achieved by a Krylov space sparse linear system solver that uses incompletely factored matrices for preconditioners. We compared two related mechanisms for parallelizing the computationally critical sparse triangular solves and sparse numeric incomplete factorizations on a range of test problems. From these comparisions we drew several interesting conclusions about methods that can be used to parallelize loops of the type found here. The performance we obtain is brought into perspective hy comparisons with timing results from a Cray X/MP supercomputer. Performance on an Encore Multimax/320 with relatively modest computational capabilities comes within a small factor of the performance on a comparable code run on a Cray X/MP.

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In many modern algorithms, relatively regular problems are encoded using flexible general purpose data structures. To obtain satisfactory performance on distributed memory architectures, it is often necessary to reconstruct and exploit the underlying dependency structure. Wel 'r' present a method to partition loops that have runtime dependencies that resemble uniform recurrence equations. Loops of this type are often found, among other places, in solving sparse triangular linear systems used for preconditioning in Krylov space iterative linear system solvers.