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Volumn 26, Issue 3, 2005, Pages 686-705

The theory of elimination trees for sparse unsymmetric matrices

Author keywords

Sparse LU decomposition; Sparse matrix factorization

Indexed keywords

SPARSE LU DECOMPOSITION; SPARSE MATRIX FACTORIZATION; SUBGRAPHS; TRIANGULAR FACTORS;

EID: 22944431546     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S089547980240563X     Document Type: Article
Times cited : (23)

References (20)
  • 1
    • 0011560546 scopus 로고
    • The transitive reduction of a directed graph
    • A. V. AHO, M. R. GAREY, AND J. D. ULLMAN, The transitive reduction of a directed graph, SIAM J. Comput., 1 (1972), pp. 131-137.
    • (1972) SIAM J. Comput. , vol.1 , pp. 131-137
    • Aho, A.V.1    Garey, M.R.2    Ullman, J.D.3
  • 3
  • 4
    • 0037265624 scopus 로고    scopus 로고
    • An unsymmetrized multifrontal LU factorization
    • P. R. AMESTOY AND C. PUGLISI, An unsymmetrized multifrontal LU factorization, SIAM J. Matrix Anal. Appl., 24 (2002), pp. 553-569.
    • (2002) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 553-569
    • Amestoy, P.R.1    Puglisi, C.2
  • 6
    • 0020822138 scopus 로고
    • The multifrontal solution of indefinite sparse symmetric linear equations
    • I. S. DUFF AND J. K. REID, The multifrontal solution of indefinite sparse symmetric linear equations, ACM Trans. Math. Software, 9 (1983), pp. 302-325.
    • (1983) ACM Trans. Math. Software , vol.9 , pp. 302-325
    • Duff, I.S.1    Reid, J.K.2
  • 7
    • 0000539027 scopus 로고
    • Exploiting structural symmetry in unsymmetric sparse symbolic factorization
    • S. C. EISENSTAT AND J. W. H. LIU, Exploiting structural symmetry in unsymmetric sparse symbolic factorization, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 202-211.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 202-211
    • Eisenstat, S.C.1    Liu, J.W.H.2
  • 8
    • 0040792814 scopus 로고
    • Structural representations of Schur complements in sparse matrices
    • A. George, J. R. Gilbert, and J. W. H. Liu, eds., Springer-Verlag, New York
    • S. C. EISENSTAT AND J. W. H. LIU, Structural representations of Schur complements in sparse matrices, in Graph Theory and Sparse Matrix Computation, A. George, J. R. Gilbert, and J. W. H. Liu, eds., Springer-Verlag, New York, 1993, pp. 85-100.
    • (1993) Graph Theory and Sparse Matrix Computation , pp. 85-100
    • Eisenstat, S.C.1    Liu, J.W.H.2
  • 9
    • 22944484394 scopus 로고    scopus 로고
    • Algorithmic aspects of elimination trees for sparse unsymmetric matrices
    • Department of Computer Science, York University, Toronto, Canada
    • S. C. EISENSTAT AND J. W. H. LIU, Algorithmic aspects of elimination trees for sparse unsymmetric matrices, Technical report, Department of Computer Science, York University, Toronto, Canada, 2004.
    • (2004) Technical Report
    • Eisenstat, S.C.1    Liu, J.W.H.2
  • 10
    • 22944441260 scopus 로고    scopus 로고
    • A tree-based dataflow model for the unsymmetric multifrontal method
    • Department of Computer Science, York University, Toronto, Canada
    • S. C. EISENSTAT AND J. W. H. LIU, A tree-based dataflow model for the unsymmetric multifrontal method, Technical report, Department of Computer Science, York University, Toronto, Canada, 2004.
    • (2004) Technical Report
    • Eisenstat, S.C.1    Liu, J.W.H.2
  • 11
    • 21144481596 scopus 로고
    • Elimination structures for unsymmetric sparse LU factors
    • J. R. GILBERT AND J. W. H. LIU, Elimination structures for unsymmetric sparse LU factors, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 334-352.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 334-352
    • Gilbert, J.R.1    Liu, J.W.H.2
  • 12
    • 0037265634 scopus 로고    scopus 로고
    • Improved symbolic and numerical factorization algorithms for unsymmetric sparse matrices
    • A. GUPTA, Improved symbolic and numerical factorization algorithms for unsymmetric sparse matrices, SIAM J. Matrix Anal. Appl., 24 (2002), pp. 529-552.
    • (2002) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 529-552
    • Gupta, A.1
  • 13
    • 0013137287 scopus 로고    scopus 로고
    • Recent advances in direct methods for solving unsymmetric sparse systems of linear equations
    • A. GUPTA, Recent advances in direct methods for solving unsymmetric sparse systems of linear equations, ACM Trans. Math. Software, 28 (2002), pp. 301-324.
    • (2002) ACM Trans. Math. Software , vol.28 , pp. 301-324
    • Gupta, A.1
  • 14
    • 0040792839 scopus 로고
    • Lost pivot recovery for an unsymmetric-pattern multifrontal method
    • University of Florida
    • S. M. HADFIELD AND T. A. D AVIS, Lost pivot recovery for an unsymmetric-pattern multifrontal method, Technical report TR-94-029, University of Florida, 1994.
    • (1994) Technical Report , vol.TR-94-029
    • Hadfield, S.M.1    Avis, T.A.D.2
  • 15
    • 84886091161 scopus 로고    scopus 로고
    • Making sparse Gaussian elimination scalable by static pivoting
    • San Jose, CA, IEEE Computer Society, Washington, DC
    • X. S. Li AND J. W. DEMMEL, Making sparse Gaussian elimination scalable by static pivoting, in Proceedings of the 1998 ACM/IEEE Conference on Supercomputing, San Jose, CA, IEEE Computer Society, Washington, DC, 1998.
    • (1998) Proceedings of the 1998 ACM/IEEE Conference on Supercomputing
    • Li, X.S.1    Demmel, J.W.2
  • 16
    • 0038621899 scopus 로고    scopus 로고
    • SuperLU DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
    • X. S. LI AND J. W. DEMMEL, SuperLU DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems, ACM Trans. Math. Software, 29 (2003), pp. 110-140.
    • (2003) ACM Trans. Math. Software , vol.29 , pp. 110-140
    • Li, X.S.1    Demmel, J.W.2
  • 17
    • 0011039373 scopus 로고
    • A tree model for sparse symmetric indefinite matrix factorization
    • J. W. H. LIU, A tree model for sparse symmetric indefinite matrix factorization, SIAM J. Matrix Anal. Appl., 9 (1988), pp. 26-39.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 26-39
    • Liu, J.W.H.1
  • 18
    • 0001450272 scopus 로고
    • The role of elimination trees in sparse factorization
    • J. W. H. Liu, The role of elimination trees in sparse factorization, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 134-172.
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , pp. 134-172
    • Liu, J.W.H.1
  • 19
    • 0001435054 scopus 로고
    • Algorithmic aspects of vertex elimination of directed graphs
    • D. J. ROSE AND R. E. TARJAN, Algorithmic aspects of vertex elimination of directed graphs, SIAM J. Appl. Math., 34(1978),pp. 176-197.
    • (1978) SIAM J. Appl. Math. , vol.34 , pp. 176-197
    • Rose, D.J.1    Tarjan, R.E.2
  • 20
    • 0020179268 scopus 로고
    • A new implementation of sparse Gaussian elimination
    • R. SCHREIBER, A new implementation of sparse Gaussian elimination, ACM Trans. Math. Software, 8(1982), pp. 256-276.
    • (1982) ACM Trans. Math. Software , vol.8 , pp. 256-276
    • Schreiber, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.