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Abstract: We propose several techniques as alternatives to partial pivoting to stabilize sparse Gaussian elimination. From numerical experiments we demonstrate that for a wide range of problems the new method is as stable as partial pivoting. The main advantage of the new method over partial pivoting is that it permits a priori determination of data structures and communication pattern, which makes it more scalable. We demonstrate the scalability of our algorithms on large-scale distributed memory... (Update)
Context of citations to this paper: More
...with other, more static techniques, can help maintain numerical stability. Li and Demmel show that such techniques are indeed possible [12]. Their proposed SuperLU DIST solver uses a 2D distribution of the sparse matrix on a 2D grid of processors and is intended for large...
.... available packages (ma41 [2, 3] and MUMPS [4, 5] and has the advantage, with respect to other unsymmetric factorization algorithms [6, 7, 21], of having the LU factorization based on the processing of an assembly tree, while the other approaches use a graph structure and or...
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0.3: A Supernodal Approach to Sparse Partial Pivoting - Demmel, Eisenstat, Gilbert.. (1995) (Correct)
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0.4: A New Scheduling Algorithm for Parallel Sparse LU Factorization .. - Grigori, Li (2002) (Correct)
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0.4: How to Eliminate Pivoting from Gaussian Elimination - By.. - Parker, Le (1995) (Correct)
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14: A fully asynchronous multifrontal solver using distributed dynamic scheduling - Amestoy, Duff et al. - 1999
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BibTeX entry: (Update)
Xiaoye S. Li and James W. Demmel. A scalable sparse direct solver using static pivoting. In Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, San Antonio, Texas, March 22--24 1999. http://citeseer.ist.psu.edu/li99scalable.html More
@inproceedings{ li99scalable,
author = "Dan Li and David R. Cheriton",
title = "Scalable Web Caching of Frequently Updated Objects Using Reliable Multicast",
booktitle = "{USENIX} Symposium on Internet Technologies and Systems",
year = "1999",
url = "citeseer.ist.psu.edu/li99scalable.html" }
Citations (may not include all citations):75 A supernodal approach to sparse partial pivoting - Demmel, Eisenstat et al. - 1995
52 Solving sparse linear systems with sparse backward error (context) - Arioli, Demmel et al. - 1989
45 An efficient block-oriented approach to parallel sparse chol.. (context) - Rothberg, Gupta - 1993
34 Elimination structures for unsymmetric sparse LU factors - Gilbert, Liu - 1993
26 An asynchronous parallel supernodal algorithm for sparse gau.. - Demmel, Gilbert et al. - 1997
25 Sparse Gaussian elimination on high performance computers - Li - 1996
18 The design and use of algorithms for permuting large entries.. - Duff, Koster - 1997
17 Message Passing Interface (context) - Interface, http et al.
12 Optimally scalable parallel sparse cholesky factorization (context) - Gupta, Kumar - 1995
7 Approximate minimum degree ordering for unsymmetric matrices (context) - Davis, Gilbert et al. - 1996
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.nersc.gov/~xiaoye/): More
Making Sparse Gaussian Elimination Scalable by Static Pivoting - Li, Demmel (1998) (Correct)
Data-level Parallel Solution of Min-cost Network Flow Problems.. - Li, Zenios (1994) (Correct)
An Asynchronous Parallel Supernodal Algorithm for Sparse.. - Demmel, Gilbert, Li (1997) (Correct)
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