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Volumn 35, Issue 3, 2008, Pages

Algorithm 887: CHOLMOD, supernodal sparse cholesky factorization and update/downdate

Author keywords

Cholesky factorization; Linear equations; Sparse matrices

Indexed keywords

CHOLESKY FACTORIZATION; CHOLESKY FACTORIZATIONS; LEVEL-3 BLAS; PEAK PERFORMANCES; POSITIVE DEFINITE; SPARSE CHOLESKY; SPARSE MATRICES; SPARSE MATRIXES; TRIANGULAR SYSTEMS;

EID: 56349128770     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1391989.1391995     Document Type: Article
Times cited : (678)

References (43)
  • 1
    • 0030491606 scopus 로고    scopus 로고
    • An approximate minimum degree ordering algorithm
    • AMESTOY, P. R., DAVIS, T. A., AND DUFF, I. S. 1996. An approximate minimum degree ordering algorithm. SIAM J. Matrix Anal. Appl. 17, 4, 886-905.
    • (1996) SIAM J. Matrix Anal. Appl , vol.17 , Issue.4 , pp. 886-905
    • AMESTOY, P.R.1    DAVIS, T.A.2    DUFF, I.S.3
  • 5
    • 56349158585 scopus 로고    scopus 로고
    • DAVIS, T. A. 1994. University of Florida sparse matrix collection. www.cise.ufl.edu/research/sparse. NA Digest, 92, no. 42.
    • DAVIS, T. A. 1994. University of Florida sparse matrix collection. www.cise.ufl.edu/research/sparse. NA Digest, vol 92, no. 42.
  • 6
    • 33745213090 scopus 로고    scopus 로고
    • Algorithm 849: A concise sparse Cholesky factorization package
    • DAVIS, T. A. 2005. Algorithm 849: A concise sparse Cholesky factorization package. ACM Trans. Math. Softw. 31, 4, 587-591.
    • (2005) ACM Trans. Math. Softw , vol.31 , Issue.4 , pp. 587-591
    • DAVIS, T.A.1
  • 8
  • 9
    • 0033239801 scopus 로고    scopus 로고
    • Modifying a sparse Cholesky factorization
    • DAVIS, T. A. AND HAGER, W. W. 1999. Modifying a sparse Cholesky factorization. SIAM J. Matrix Anal. Appl. 20, 3, 606-627.
    • (1999) SIAM J. Matrix Anal. Appl , vol.20 , Issue.3 , pp. 606-627
    • DAVIS, T.A.1    HAGER, W.W.2
  • 10
    • 0035537394 scopus 로고    scopus 로고
    • Multiple-rank modifications of a sparse Cholesky factorization
    • DAVIS, T. A. AND HAGER, W. W. 2001. Multiple-rank modifications of a sparse Cholesky factorization. SIAM J. Matrix Anal. Appl. 22, 997-1013.
    • (2001) SIAM J. Matrix Anal. Appl , vol.22 , pp. 997-1013
    • DAVIS, T.A.1    HAGER, W.W.2
  • 11
    • 36749099985 scopus 로고    scopus 로고
    • DAVIS, T. A. AND HAGER, W. W. 2007a. Dual multilevel optimization. Math. Program. 112, 2 (Nov.), 403-425.
    • DAVIS, T. A. AND HAGER, W. W. 2007a. Dual multilevel optimization. Math. Program. 112, 2 (Nov.), 403-425.
  • 12
    • 36749081650 scopus 로고    scopus 로고
    • DAVIS, T. A. AND HAGER, W. W. 2007b. A sparse proximal implementation of the LP Dual Active Set Algorithm. Math. Program. 112, 2 (Nov.), 275-301.
    • DAVIS, T. A. AND HAGER, W. W. 2007b. A sparse proximal implementation of the LP Dual Active Set Algorithm. Math. Program. 112, 2 (Nov.), 275-301.
  • 13
    • 56349122415 scopus 로고    scopus 로고
    • Dynamic supernodes in sparse Cholesky update/downdate and triangular solves
    • to appear
    • DAVIS, T. A. AND HAGER, W. W. 2009. Dynamic supernodes in sparse Cholesky update/downdate and triangular solves. ACM Trans. Math. Softw., to appear.
    • (2009) ACM Trans. Math. Softw
    • DAVIS, T.A.1    HAGER, W.W.2
  • 14
    • 33745312905 scopus 로고    scopus 로고
    • The design of sparse direct solvers using object oriented techniques
    • Advances in Software Tools for Scientific Computing, H. P. Langtangen, A. M. Bruaset, and E. Quak, Eds, Springer-Verlag, Berlin
    • DOBRIAN, F., KUMFERT, G. K., AND POTHEN, A. 2000. The design of sparse direct solvers using object oriented techniques. In Advances in Software Tools for Scientific Computing, H. P. Langtangen, A. M. Bruaset, and E. Quak, Eds. Lecture Notes in Computational Science and Engineering, vol. 10. Springer-Verlag, Berlin, 89-131.
    • (2000) Lecture Notes in Computational Science and Engineering , vol.10 , pp. 89-131
    • DOBRIAN, F.1    KUMFERT, G.K.2    POTHEN, A.3
  • 19
    • 0042318563 scopus 로고    scopus 로고
    • Computing row and column counts for sparse QR and LU factorization
    • GILBERT, J. R., LI, X. S., NG, E. G., AND PEYTON, B. W. 2001. Computing row and column counts for sparse QR and LU factorization. BIT 41, 4, 693-710.
    • (2001) BIT 41 , vol.4 , pp. 693-710
    • GILBERT, J.R.1    LI, X.S.2    NG, E.G.3    PEYTON, B.W.4
  • 20
    • 0000470989 scopus 로고
    • Sparse matrices in MATLAB: Design and implementation
    • GILBERT, J. R., MOLER, C., AND SCHREIBER, R. 1992. Sparse matrices in MATLAB: design and implementation. SIAM J. Matrix Anal. Appl. 13, 1, 333-356.
    • (1992) SIAM J. Matrix Anal. Appl , vol.13 , Issue.1 , pp. 333-356
    • GILBERT, J.R.1    MOLER, C.2    SCHREIBER, R.3
  • 21
    • 21844496297 scopus 로고
    • An efficient algorithm to compute row and column counts for sparse Cholesky factorization
    • GILBERT, J. R., NG, E. G., AND PEYTON, B. W. 1994. An efficient algorithm to compute row and column counts for sparse Cholesky factorization. SIAM J. Matrix Anal. Appl. 15, 4, 1075-1091.
    • (1994) SIAM J. Matrix Anal. Appl , vol.15 , Issue.4 , pp. 1075-1091
    • GILBERT, J.R.1    NG, E.G.2    PEYTON, B.W.3
  • 22
    • 84966204836 scopus 로고
    • Methods for modifying matrix factorizations
    • GILL, P. E., GOLUB, G. H., MURRAY, W., AND SAUNDERS, M. A. 1974. Methods for modifying matrix factorizations. Math. Comp. 28, 126, 505-535.
    • (1974) Math. Comp , vol.28 , Issue.126 , pp. 505-535
    • GILL, P.E.1    GOLUB, G.H.2    MURRAY, W.3    SAUNDERS, M.A.4
  • 23
    • 34249828455 scopus 로고    scopus 로고
    • Introduction to the Intel core duo processor architecture
    • GOCHMAN, S., MENDELSON, A., NAVEH, A., AND ROTEM, E. 2006. Introduction to the Intel core duo processor architecture. Intel Techn. J. 10, 2, 89-98.
    • (2006) Intel Techn. J , vol.10 , Issue.2 , pp. 89-98
    • GOCHMAN, S.1    MENDELSON, A.2    NAVEH, A.3    ROTEM, E.4
  • 24
    • 85121159800 scopus 로고    scopus 로고
    • GOTO, K. AND VAN DE GEIJN, R. 2008. High performance implementation of the level-3 BLAS. ACM Trans. Math. Softw. 35, 1.
    • GOTO, K. AND VAN DE GEIJN, R. 2008. High performance implementation of the level-3 BLAS. ACM Trans. Math. Softw. 35, 1.
  • 25
    • 56349108463 scopus 로고    scopus 로고
    • GOULD, N. I. M., HU, Y., AND SCOTT, J. A. 2006. Complete results from a numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations. Tech. Rep. Internal report 2005-1 (revision 2), CCLRC, Rutherford Appleton Laboratory. (Mar.)
    • GOULD, N. I. M., HU, Y., AND SCOTT, J. A. 2006. Complete results from a numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations. Tech. Rep. Internal report 2005-1 (revision 2), CCLRC, Rutherford Appleton Laboratory. (Mar.)
  • 26
    • 34547483006 scopus 로고    scopus 로고
    • A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations
    • June, 32 pages
    • GOULD, N. I. M., HU, Y., AND SCOTT, J. A. 2007. A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations. ACMTrans. Math. Softw. 33, 2 (June), 32 pages.
    • (2007) ACMTrans. Math. Softw , vol.33 , Issue.2
    • GOULD, N.I.M.1    HU, Y.2    SCOTT, J.A.3
  • 27
    • 33745328283 scopus 로고    scopus 로고
    • WSMP: A high-performance serial and parallel sparse linear solver
    • 22038 98932, IBM T.J. Watson Research Center
    • GUPTA, A., JOSHI, M., AND KUMAR, V. 2001. WSMP: A high-performance serial and parallel sparse linear solver. Tech. Rep. RC 22038 (98932), IBM T.J. Watson Research Center.
    • (2001) Tech. Rep. RC
    • GUPTA, A.1    JOSHI, M.2    KUMAR, V.3
  • 28
    • 0031140712 scopus 로고    scopus 로고
    • Highly scalable parallel algorithms for sparse matrix factorization
    • GUPTA, A., KARYPIS, G., AND KUMAR, V. 1997. Highly scalable parallel algorithms for sparse matrix factorization. IEEE Trans. Para. Distrib. Syst. 8, 5, 502-520.
    • (1997) IEEE Trans. Para. Distrib. Syst , vol.8 , Issue.5 , pp. 502-520
    • GUPTA, A.1    KARYPIS, G.2    KUMAR, V.3
  • 29
    • 0024682770 scopus 로고
    • Updating the inverse of a matrix
    • HAGER, W. W. 1989. Updating the inverse of a matrix. SIAM Rev. 31, 2, 221-239.
    • (1989) SIAM Rev , vol.31 , Issue.2 , pp. 221-239
    • HAGER, W.W.1
  • 30
    • 0036467470 scopus 로고    scopus 로고
    • PaStiX: A high-performance parallel direct solver for sparse symmetric definite systems
    • HÉNON, P., RAMET, P., AND ROMAN, J. 2002. PaStiX: A high-performance parallel direct solver for sparse symmetric definite systems. Para. Comput. 28, 2, 301-321.
    • (2002) Para. Comput , vol.28 , Issue.2 , pp. 301-321
    • HÉNON, P.1    RAMET, P.2    ROMAN, J.3
  • 31
    • 0032131147 scopus 로고    scopus 로고
    • A fast and high quality multilevel scheme for partitioning irregular graphs
    • KARYPIS, G. AND KUMAR, V. 1998. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20, 359-392.
    • (1998) SIAM J. Sci. Comput , vol.20 , pp. 359-392
    • KARYPIS, G.1    KUMAR, V.2
  • 33
    • 0022077450 scopus 로고
    • Modification of the minimum-degree algorithm by multiple elimination
    • LIU, J. W. H. 1985. Modification of the minimum-degree algorithm by multiple elimination. ACM Trans. Math. Softw. 11, 2, 141-153.
    • (1985) ACM Trans. Math. Softw , vol.11 , Issue.2 , pp. 141-153
    • LIU, J.W.H.1
  • 34
    • 0001450272 scopus 로고
    • The role of elimination trees in sparse factorization
    • LIU, J. W. H. 1990. The role of elimination trees in sparse factorization. SIAM J. Matrix Anal. Appl. 11, 1, 134-172.
    • (1990) SIAM J. Matrix Anal. Appl , vol.11 , Issue.1 , pp. 134-172
    • LIU, J.W.H.1
  • 35
    • 56349156488 scopus 로고    scopus 로고
    • Cleve's corner: Parallel MATLAB: multiple processors and multiple cores
    • MOLER, C. June 2007. Cleve's corner: parallel MATLAB: multiple processors and multiple cores. MATLAB News and Notes.
    • (2007) MATLAB News and Notes
    • MOLER1    June, C.2
  • 36
    • 0000018801 scopus 로고
    • Block sparse Cholesky algorithms on advanced uniprocessor computers
    • NG, E. G. AND PEYTON, B. W. 1993. Block sparse Cholesky algorithms on advanced uniprocessor computers. SIAM J. Sci. Comput. 14, 5, 1034-1056.
    • (1993) SIAM J. Sci. Comput , vol.14 , Issue.5 , pp. 1034-1056
    • NG, E.G.1    PEYTON, B.W.2
  • 37
    • 0033716826 scopus 로고    scopus 로고
    • Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering
    • PELLEGRINI, F., ROMAN, J., AND AMESTOY, P. R. 2000. Hybridizing nested dissection and halo approximate minimum degree for efficient sparse matrix ordering. Concurrency: Pract. Exp. 12, 68-84.
    • (2000) Concurrency: Pract. Exp , vol.12 , pp. 68-84
    • PELLEGRINI, F.1    ROMAN, J.2    AMESTOY, P.R.3
  • 38
    • 0032397942 scopus 로고    scopus 로고
    • Node selection strategies for bottom-up sparse matrix orderings
    • ROTHBERG, E. AND EISENSTAT, S. C. 1998. Node selection strategies for bottom-up sparse matrix orderings. SIAM J. Matrix Anal. Appl. 19, 3, 682-695.
    • (1998) SIAM J. Matrix Anal. Appl , vol.19 , Issue.3 , pp. 682-695
    • ROTHBERG, E.1    EISENSTAT, S.C.2
  • 39
    • 0026214508 scopus 로고
    • Efficient sparse matrix factorization on high-performance workstations-exploiting the memory hierarchy
    • ROTHBERG, E. AND GUPTA, A. 1991. Efficient sparse matrix factorization on high-performance workstations-exploiting the memory hierarchy. ACM Trans. Math. Softw. 17, 3, 313-334.
    • (1991) ACM Trans. Math. Softw , vol.17 , Issue.3 , pp. 313-334
    • ROTHBERG, E.1    GUPTA, A.2
  • 40
    • 2442521453 scopus 로고    scopus 로고
    • The design and implementation of a new out-of-core sparse Cholesky factorization method
    • ROTKIN, V. AND TOLEDO, S. 2004. The design and implementation of a new out-of-core sparse Cholesky factorization method. ACM Trans. Math. Softw. 30, 1, 19-46.
    • (2004) ACM Trans. Math. Softw , vol.30 , Issue.1 , pp. 19-46
    • ROTKIN, V.1    TOLEDO, S.2
  • 41
    • 34548731368 scopus 로고    scopus 로고
    • Experiences of sparse direct symmetric solvers
    • SCOTT, J. A. AND HU, Y. 2007. Experiences of sparse direct symmetric solvers. ACM Trans. Math. Softw. 33, 3.
    • (2007) ACM Trans. Math. Softw , vol.33 , pp. 3
    • SCOTT, J.A.1    HU, Y.2
  • 42
    • 0000672950 scopus 로고
    • The effects of rounding error on an algorithm for downdating a Cholesky factorization
    • STEWART, G. W. 1979. The effects of rounding error on an algorithm for downdating a Cholesky factorization. J. Inst. Math. Appl. 23, 203-213.
    • (1979) J. Inst. Math. Appl , vol.23 , pp. 203-213
    • STEWART, G.W.1
  • 43
    • 33748875998 scopus 로고    scopus 로고
    • Matrix algorithms
    • SIAM, Philadelphia
    • STEWART, G. W. 1998. Matrix algorithms, Volume 1: Basic decompositions. SIAM, Philadelphia.
    • (1998) Basic decompositions , vol.1
    • STEWART, G.W.1


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