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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 that is valid irrespective of the amount of dynamic pivoting performed during numerical factorization. Finally, we describe an... (Update)
Context of citations to this paper: More
.... sparse solver packages can be found in [6] A discussion of the algorithms used in WSMP for solving general sparse systems can be found in [7, 5]. Currently, WSMP does not support the solution of general unsymmetric sparse systems in a messagepassing parallel environment. WSMP...
.... and algorithms to accommodate these ll ins [3] or else use static data structures which can grossly overestimate the true ll in [26, 35]. The second complication is the need to handle two factored matrices L and U , which are structurally di erent yet closely related to...
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WSMP: Watson Sparse Matrix Package Part II - direct . . . - Gupta (2000) (Correct)
SuperLU DIST: A Scalable Distributed-Memory Sparse Direct.. - Li, Demmel (2002) (Correct)
WSMP: Watson Sparse Matrix Package Part II - direct solution of.. - Gupta (2000) (Correct)
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0.4: An Unsymmetrized Multifrontal LU Factorization - Amestoy, Puglisi (2000) (Correct)
0.4: Improved Symbolic and Numerical Factorization Algorithms for.. - Gupta (2002) (Correct)
0.2: Analysis, Tuning and Comparison of Two General Sparse .. - Amestoy, Duff.. (2000) (Correct)
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2.3: WSMP: Watson Sparse Matrix Package Part I - direct solution of.. - Gupta (2000) (Correct)
1.0: Graph Partitioning Based Sparse Matrix Orderings for.. - Gupta (1996) (Correct)
0.5: Symmetric Orderings for Unsymmetric Sparse Matrices - Wijshoff (1991) (Correct)
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3: WSMP: Watson Sparse Matrix Package (context) - Gupta - 2000
3: Making Sparse Gaussian Elimination Scalable by Static Pivoting - Li, Demmel - 1998
3: A new pivoting strategy for Gaussian elimination - Olschowka, Neumaier - 1996
BibTeX entry: (Update)
Anshul Gupta. Improved symbolic and numerical factorization algorithms for unsymmetric sparse matrices. Technical Report RC 22137 (99131), IBM T. J. Watson Research Center, Yorktown Heights, NY, August 1, 2001. http://www.cs.umn.edu/~agupta/doc/sparse-unsymm.ps. http://citeseer.ist.psu.edu/article/gupta01improved.html More
@article{ gupta01improved,
author = "Anupam Gupta",
title = "Improved Bandwidth Approximation for Trees and Chordal Graphs",
journal = "J. Algorithms",
volume = "40",
number = "1",
pages = "24-36",
year = "2001",
url = "citeseer.ist.psu.edu/article/gupta01improved.html" }
Citations (may not include all citations):126 The role of elimination trees in sparse factorization (context) - Liu - 1990
98 An approximate minimum degree ordering algorithm - Davis, Amestoy et al. - 1996
63 An unsymmetric-pattern multifrontal method for sparse LU fac.. - Davis, Duff - 1997
57 Highly scalable parallel algorithms for sparse matrix factor.. - Gupta, Karypis et al. - 1997
57 The multifrontal solution of unsymmetric sets of linear equa.. (context) - Duff, Reid - 1984
57 The multifrontal method for sparse matrix solution: Theory a.. (context) - Liu - 1992
56 Vectorization of a multiprocessor multifrontal code (context) - Amestoy, Duff - 1989
45 Direct Methods for Sparse Matrices (context) - Duff, Erisman et al. - 1990
40 Multifrontal parallel distributed symmetric and unsymmetric .. - Amestoy, Duff et al. - 2000
39 Fast and effective algorithms for graph partitioning and spa.. - Gupta - 1997
34 Elimination structures for unsymmetric sparse LU factors - Gilbert, Liu - 1993
32 A fully asynchronous multifrontal solver using distributed d.. - Amestoy, Duff et al. - 2001
30 The influence of relaxed supernode partitions on the multifr.. (context) - Ashcraft, Grimes - 1989
23 On algorithms for permuting large entries to the diagonal of.. - Duff, Koster
17 Exploiting structural symmetry in unsymmetric sparse symboli.. (context) - Eisenstat, Liu - 1992
15 A scalable sparse direct solver using static pivoting - Li, Demmel - 1999
14 A supernodal approach to sparse partial pivoting (context) - Demmel, Eisenstat et al. - 1999
13 A column approximate minimum degree ordering algorithm - Davis, Gilbert et al. - 2000
7 the LU Factorization of Sequences of Identically Structured .. - Hadfield - 1994
1 UMFPACK software for unsymmetric multifrontal method (context) - Davis - 2001
1 An experimental comparison of some direct sparse solver pack.. (context) - Gupta, Muliadi - 2001
1 and comparison of two general sparse solvers for distributed.. (context) - Amestoy, Duff et al. - 2000
Documents on the same site (http://www-users.cs.umn.edu/~agupta/wsmp.html): More
Recent Advances in Direct Methods for Solving Unsymmetric Sparse.. - Gupta (2001) (Correct)
WSMP: A High-Performance Shared- and Distributed-Memory.. - Gupta, Joshi (2001) (Correct)
A Highly Scalable Parallel Algorithm for Sparse Matrix.. - Gupta, Karypis, Kumar (1995) (Correct)
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