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Abstract: . The elimination tree is central to the study of Cholesky factorization of sparse symmetric positive definite matrices. In this paper, we generalize the elimination tree to a structure appropriate for the sparse LU factorization of unsymmetric matrices. We define a pair of directed acyclic graphs called elimination dags, and use them to characterize the zero-nonzero structures of the lower and upper triangular factors. We apply these elimination structures in a new algorithm to compute fill... (Update)
Context of citations to this paper: More
.... the minimum graph representations of the L and U factors are directed acyclic graphs (called elimination DAGs, or edags for short) [31, 32]. Despite these diculties, researchers have been addressing these issues successfully for sequential and shared memory machines;...
.... way to represent the symbolic LU factorization of a structurally unsymmetric matrix is to use directed acyclic graphs (see for example [17, 18]) These This work was supported by the Director, Oce of Science, Division of Mathematical, Information, and Computational Sciences...
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22: The Role of Elimination Trees in Sparse Factorization (context) - Liu - 1990
15: A supernodal approach to sparse partial pivoting - Demmel, Eisenstat et al. - 1995
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BibTeX entry: (Update)
J. R. Gilbert and J. W. H. Liu. Elimination structures for unsymmetric sparse LU factors. SIAM J. Matrix Analysis and Applications, 14:334--352, 1993. http://citeseer.ist.psu.edu/gilbert93elimination.html More
@techreport{ gilbert90elimination,
author = "{Gilbert, J. R.} and {Liu, J. W. H.}",
title = "Elimination Structures for Unsymmetric Sparse {LU} Factors",
number = "CS-90-11",
address = "North York, Ontario",
year = "1990",
url = "citeseer.ist.psu.edu/gilbert93elimination.html" }
Citations (may not include all citations):452 Data Structures and Algorithms (context) - Aho, Hopcroft et al. - 1983 ACM
346 Computer Solution of Large Sparse Positive Definite Systems (context) - George, Liu - 1981
126 The role of elimination trees in sparse factorization (context) - Liu - 1990 ACM
73 Triangulated graphs and the elimination process (context) - Rose - 1970
72 Sparse matrices in Matlab: Design and implementation - Gilbert, Moler et al. - 1991
62 The transitive reduction of a directed graph (context) - Aho, Garey et al. - 1972 DBLP
47 ACM Transactions on Mathematical Software (context) - Duff, Grimes et al. - 1989
39 Predicting structure in sparse matrix computations - Gilbert - 1986 ACM
31 Sparse partial pivoting in time proportional to arithmetic o.. (context) - Gilbert, Peierls - 1988 ACM
30 A new implementation of sparse Gaussian elimination (context) - Schreiber - 1982 ACM
17 Exploiting structural symmetry in unsymmetric sparse symboli.. (context) - Eisenstat, Liu - 1990 ACM
13 A compact row storage scheme for Cholesky factors using elim.. (context) - Liu - 1986 ACM
12 Exploiting structural symmetry in a sparse partial pivoting .. (context) - Eisenstat, Liu - 1991 ACM
8 Algorithmic aspects of vertex elimination of directed graphs (context) - Rose, Tarjan - 1978
The graph only includes citing articles where the year of publication is known.
Documents on the same site (ftp://parcftp.xerox.com/pub/gilbert/index.html): More
Separators in Graphs with Negative and Multiple Vertex Weights - Djidjev, Gilbert (1994) (Correct)
Separators and Structure Prediction in Sparse Orthogonal.. - Gilbert, Ng, Peyton (1993) (Correct)
Predicting Structure In Nonsymmetric Sparse Matrix Factorizations - Gilbert, Ng (1992) (Correct)
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