Copyright © [2002] by The Society for Industrial and Applied Mathematics. All rights reserved
We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations. We have modified a classical symbolic factorization algorithm for unsymmetric matrices to inexpensively compute minimal elimination structures. We give an efficient algorithm to compute a near-minimal data-dependency graph that is valid irrespective of the amount of dynamic pivoting performed during numerical factorization. Finally, we describe an unsymmetric-pattern multifrontal algorithm for Gaussian elimination with partial pivoting that uses the task- and data-dependency graphs computed during the symbolic phase. These algorithms have been implemented in WSMP---an industrial strength sparse solver package---and have enabled WSMP to significantly outperform other similar solvers. We present experimental results to demonstrate the merits of the new algorithms.
By: Anshul Gupta
Published in: SIAM Journal on Matrix Analysis and Applications , volume 24, (no 2), pages 529-52 in 2002
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