메뉴 건너뛰기




Volumn 20, Issue 4, 1999, Pages 915-952

An asynchronous parallel supernodal algorithm for sparse Gaussian elimination

Author keywords

Dynamic scheduling and load balancing; Parallelism; Sparse Gaussian elimination; Supernodes; Unsymmetric linear systems

Indexed keywords


EID: 0033242228     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479897317685     Document Type: Article
Times cited : (200)

References (34)
  • 3
    • 0024901312 scopus 로고
    • The influence of relaxed supernode partitions on the multifrontal method
    • C. ASHCRAFT AND R. GRIMES, The influence of relaxed supernode partitions on the multifrontal method, ACM Trans. Math. Software, 15 (1989), pp. 291-309.
    • (1989) ACM Trans. Math. Software , vol.15 , pp. 291-309
    • Ashcraft, C.1    Grimes, R.2
  • 4
    • 24344465959 scopus 로고    scopus 로고
    • Optimizing matrix multiply using PHiPAC: A portable, high-performance, ANSI C coding methodology
    • Technical report CS-96-326, Computer Science Dept., University of Tennessee, Knoxville, TN, May
    • J. BILMES, K. ASANOVIC, J. DEMMEL, D. LAM, AND C.-W. CHIN, Optimizing Matrix Multiply Using PHiPAC: A Portable, High-performance, ANSI C Coding Methodology, Technical report CS-96-326, Computer Science Dept., University of Tennessee, Knoxville, TN, May 1996 (LAPACK Working Note 111).
    • (1996) LAPACK Working Note 111
    • Bilmes, J.1    Asanovic, K.2    Demmel, J.3    Lam, D.4    Chin, C.-W.5
  • 5
    • 0009170244 scopus 로고
    • A nondeterministic parallel algorithm for general unsymmetric sparse LU factorization
    • T. A. DAVIS AND P.-C. YEW, A nondeterministic parallel algorithm for general unsymmetric sparse LU factorization, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 383-402.
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , pp. 383-402
    • Davis, T.A.1    Yew, P.-C.2
  • 10
    • 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
  • 11
    • 0000165006 scopus 로고
    • Exploiting structural symmetry in a sparse partial pivoting code
    • S. C. EISENSTAT AND J. W.H. LIU, Exploiting structural symmetry in a sparse partial pivoting code, SIAM J. Sci. Comput., 14 (1993), pp. 253-257.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 253-257
    • Eisenstat, S.C.1    Liu, J.W.H.2
  • 13
    • 0009167398 scopus 로고
    • Solution of sparse positive definitive systems on a shared-memory multiprocessor
    • A. GEORGE, M. T. HEATH, J. LIU, AND E. NG, Solution of sparse positive definitive systems on a shared-memory multiprocessor, Internat. J. Parallel Programming, 15 (1986), pp. 309-325.
    • (1986) Internat. J. Parallel Programming , vol.15 , pp. 309-325
    • George, A.1    Heath, M.T.2    Liu, J.3    Ng, E.4
  • 14
    • 0001868413 scopus 로고
    • A data structure for sparse QR and LU factorizations
    • A. GEORGE, J. LIU, AND E. NG, A data structure for sparse QR and LU factorizations, SIAM J. Sci. Stat. Comput., 9 (1988), pp. 100-121.
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 100-121
    • George, A.1    Liu, J.2    Ng, E.3
  • 15
    • 0001721072 scopus 로고
    • An implementation of Gaussian elimination with partial pivoting for sparse systems
    • A. GEORGE AND E. NG, An implementation of Gaussian elimination with partial pivoting for sparse systems, SIAM J. Sci. Stat. Comput., 6 (1985), pp. 390-409.
    • (1985) SIAM J. Sci. Stat. Comput. , vol.6 , pp. 390-409
    • George, A.1    Ng, E.2
  • 16
    • 0000657206 scopus 로고
    • Symbolic factorization for sparse Gaussian elimination with partial pivoting
    • A. GEORGE AND E. NG, Symbolic factorization for sparse Gaussian elimination with partial pivoting, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 877-898.
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , pp. 877-898
    • George, A.1    Ng, E.2
  • 17
    • 0000980815 scopus 로고
    • Parallel sparse Gaussian elimination with partial pivoting
    • A. GEORGE AND E. NG, Parallel sparse Gaussian elimination with partial pivoting, Ann. Oper. Res., 22 (1990), pp. 219-240.
    • (1990) Ann. Oper. Res. , vol.22 , pp. 219-240
    • George, A.1    Ng, E.2
  • 18
  • 19
    • 0000215640 scopus 로고
    • Predicting structure in nonsymmetric sparse matrix factorizations
    • A. George, J. R. Gilbert, and J. W. H. Liu, eds., Springer-Verlag, New York
    • J. R. GILBERT AND E. G. NG, Predicting structure in nonsymmetric sparse matrix factorizations, in Graph Theory and Sparse Matrix Computation, A. George, J. R. Gilbert, and J. W. H. Liu, eds., Springer-Verlag, New York, 1993, pp. 107-139.
    • (1993) Graph Theory and Sparse Matrix Computation , pp. 107-139
    • Gilbert, J.R.1    Ng, E.G.2
  • 21
    • 85033951892 scopus 로고
    • Computing row and column counts for sparse QR factorization
    • Snowbird, UT, June; journal version in preparation
    • J. R. GILBERT, E. G. NG, AND B. W. PEYTON, Computing row and column counts for sparse QR factorization, talk presented at Fifth SIAM Conference on Applied Linear Algebra, Snowbird, UT, June 1994; journal version in preparation.
    • (1994) Fifth SIAM Conference on Applied Linear Algebra
    • Gilbert, J.R.1    Ng, E.G.2    Peyton, B.W.3
  • 22
    • 21844496297 scopus 로고
    • An efficient algorithm to compute row and column counts for sparse cholesky factorization
    • J. R. GILBERT, E. G. NG, AND B. W. PEYTON, An efficient algorithm to compute row and column counts for sparse Cholesky factorization, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 1075-1091.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 1075-1091
    • Gilbert, J.R.1    Ng, E.G.2    Peyton, B.W.3
  • 24
    • 0003389362 scopus 로고
    • Parallel sparse Cholesky factorization algorithms for shared-memory multiprocessor systems
    • R. Vichnevetsky, D. Knight, and G. Richter, eds., IMACS, New Brunswick, NJ
    • A. GUPTA, E. ROTHBERG, E. NG. AND B. W. PEYTON, Parallel sparse Cholesky factorization algorithms for shared-memory multiprocessor systems, in Advances in Computer Methods for Partial Differential Equations-VII, R. Vichnevetsky, D. Knight, and G. Richter, eds., IMACS, New Brunswick, NJ, 1992, pp. 622-628.
    • (1992) Advances in Computer Methods for Partial Differential Equations-VII , pp. 622-628
    • Gupta, A.1    Rothberg, E.2    Ng, E.3    Peyton, B.W.4
  • 25
    • 0003950261 scopus 로고    scopus 로고
    • Technical report UCB//CSD-96-919 and Ph.D. thesis, Computer Science Division, University of California, Berkeley, CA, September
    • X. S. LI, Sparse Gaussian Elimination on High Performance Computers, Technical report UCB//CSD-96-919 and Ph.D. thesis, Computer Science Division, University of California, Berkeley, CA, September 1996.
    • (1996) Sparse Gaussian Elimination on High Performance Computers
    • Li, X.S.1
  • 26
    • 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
  • 27
    • 21144482411 scopus 로고
    • On finding supernodes for sparse matrix computations
    • J. W. H. LIU, E. G. NG, AND B. W. PEYTON, On finding supernodes for sparse matrix computations, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 242-252.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 242-252
    • Liu, J.W.H.1    Ng, E.G.2    Peyton, B.W.3
  • 28
    • 0000817412 scopus 로고
    • A supernodal Cholesky factorization algorithm for shared-memory multiprocessors
    • E. NG AND B. W. PEYTON, A supernodal Cholesky factorization algorithm for shared-memory multiprocessors, SIAM J. Sci. Comput., 14 (1993), pp. 761-769.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 761-769
    • Ng, E.1    Peyton, B.W.2
  • 29
    • 0001102965 scopus 로고    scopus 로고
    • Performance of panel and block approaches to sparse Cholesky factorization on the iPSC/860 and paragon multicomputers
    • E. ROTHBERG, Performance of panel and block approaches to sparse Cholesky factorization on the iPSC/860 and Paragon multicomputers, SIAM J. Sci. Comput., 17 (1996), pp. 699-713.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 699-713
    • Rothberg, E.1
  • 30
    • 85033970608 scopus 로고
    • Technical report, Silicon Graphics, Mountain View, CA
    • SGI Power Challenge, Technical report, Silicon Graphics, Mountain View, CA, 1995.
    • (1995) SGI Power Challenge
  • 31
    • 85033972647 scopus 로고
    • Technical white paper, Sun Microsystems, Inc., Mountain View, CA, November
    • SPARCcenter 2000 architecture and implementation, Technical white paper, Sun Microsystems, Inc., Mountain View, CA, November 1993.
    • (1993) SPARCcenter 2000 Architecture and
  • 32
    • 1542745115 scopus 로고    scopus 로고
    • Stable finite elements for problems with wild coefficients
    • S. A. VAVASIS, Stable finite elements for problems with wild coefficients, SIAM J. Numer. Anal., 33 (1996), pp. 809-916.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 809-916
    • Vavasis, S.A.1
  • 33
    • 85033950088 scopus 로고    scopus 로고
    • Cray Research, Inc., Eagen, MN
    • The Cray C90 series, Cray Research, Inc., Eagen, MN, http://www.cray.com/swpubs/
    • The Cray C90 Series
  • 34
    • 85033951509 scopus 로고    scopus 로고
    • Cray Research, Inc., Eagen, MN
    • The Cray J90 series, Cray Research, Inc., Eagen, MN, http://www.cray.com/swpubs/
    • The Cray J90 Series


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.