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The LU Factorization

  Following the philosophy of Harwell's MA28, we have interfaced a new concurrent sparse solver to Concurrent DASSL, the details of which are quoted elsewhere in this proceedings [Skjellum:90d]. In short, there is a two-step factorization procedure: A-mode, which chooses stable pivots according to a user-specified function, and builds the sparse data structures dynamically; and B-mode, which reuses the data structures and pivot sequence on a similar matrix, but monitors stability with a growth-factor test. A-mode is repeated whenever necessary to avoid instability. We expect subcubic time complexity and subquadratic space complexity in N for the sparse solver. We attain acceptable factorization speedups for systems that are not narrow banded, and of sufficient size. We intend to incorporate multiple pivoting heuristic strategies, following [Alaghband:89a], to further improve performance of future versions of the solver. This may also contribute to better performance of the triangular solves.

Guy Robinson
Wed Mar 1 10:19:35 EST 1995