NDLI: Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matrices

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Gupta, Anshul
Copyright Year	2002
Abstract	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 for unsymmetric multifrontal factorization that is valid irrespective of the amount of dynamic pivoting performed during 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.
Starting Page	529
Ending Page	552
Page Count	24
File Format	PDF
ISSN	08954798
DOI	10.1137/S089547980139604X
e-ISSN	10957162
Journal	SIAM Journal on Matrix Analysis and Applications (SJMAEL)
Issue Number	2
Volume Number	24
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	Graphs and linear algebra sparse matrix factorization Direct methods for linear systems and matrix inversion Parallel computation multifrontal methods Sparse matrices parallel sparse solvers
Content Type	Text
Resource Type	Article
Subject	Analysis

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