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Volumn 22, Issue 10, 1996, Pages 1291-1333

Solving large nonsymmetric sparse linear systems using MCSPARSE

Author keywords

Cedar system; Implementation; Linear algebra; Parallel processing systems; Sparse linear systems

Indexed keywords

HIERARCHICAL SYSTEMS; MATHEMATICAL TECHNIQUES; PARALLEL PROCESSING SYSTEMS; SYSTEM STABILITY;

EID: 0030421529     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8191(96)00047-6     Document Type: Article
Times cited : (10)

References (48)
  • 1
    • 0024961186 scopus 로고
    • Parallel pivoting combined with parallel reduction and fill-in control
    • G. Alaghband, Parallel pivoting combined with parallel reduction and fill-in control, Parallel Computing 11 (1989) 201-221.
    • (1989) Parallel Computing , vol.11 , pp. 201-221
    • Alaghband, G.1
  • 2
    • 2942632591 scopus 로고
    • Experiments in tearing large sparse systems
    • M.G. Cox and S. Hammarling, eds., Oxford University Press, New York
    • M. Arioli and I.S. Duff, Experiments in tearing large sparse systems, in: M.G. Cox and S. Hammarling, eds., Reliable Numerical Computation (Oxford University Press, New York, 1990) 207-226.
    • (1990) Reliable Numerical Computation , pp. 207-226
    • Arioli, M.1    Duff, I.S.2
  • 4
    • 84972716214 scopus 로고
    • Progress in sparse matrix methods for large linear systems on vector supercomputers, Internat
    • C.C. Ashcraft, R.G. Grimes, J.G. Lewis, B.W. Peyton and H.D. Simon, Progress in sparse matrix methods for large linear systems on vector supercomputers, Internat. J. Supercomputing Appl. 1 (4) (1987) 10-30.
    • (1987) J. Supercomputing Appl. , vol.1 , Issue.4 , pp. 10-30
    • Ashcraft, C.C.1    Grimes, R.G.2    Lewis, J.G.3    Peyton, B.W.4    Simon, H.D.5
  • 5
    • 0016116944 scopus 로고
    • Analysis of sparse elimination
    • J.R. Bunch, Analysis of sparse elimination, SIAM J. Numer. Anal. 11 (5) (1974) 847-873.
    • (1974) SIAM J. Numer. Anal. , vol.11 , Issue.5 , pp. 847-873
    • Bunch, J.R.1
  • 6
    • 0016102206 scopus 로고
    • The bordered triangular matrix and minimum essential sets of a digraph
    • L.K. Cheung and E.S. Kuh, The bordered triangular matrix and minimum essential sets of a digraph, IEEE Trans. Circuits Systems 21 (5) (1974) 633-639.
    • (1974) IEEE Trans. Circuits Systems , vol.21 , Issue.5 , pp. 633-639
    • Cheung, L.K.1    Kuh, E.S.2
  • 8
    • 0024135952 scopus 로고
    • Pairwise reduction for the direct, parallel solution of sparse unsymmetric sets of linear equations
    • T.A. Davis and E.S. Davidson, Pairwise reduction for the direct, parallel solution of sparse unsymmetric sets of linear equations, IEEE Trans. Comput. 37 (12) (1988) 1648-1654.
    • (1988) IEEE Trans. Comput. , vol.37 , Issue.12 , pp. 1648-1654
    • Davis, T.A.1    Davidson, E.S.2
  • 9
    • 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 (3) (1990) 383-402.
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , Issue.3 , pp. 383-402
    • Davis, T.A.1    Yew, P.C.2
  • 10
    • 84976724340 scopus 로고
    • Algorithm 575, Permutations for a zero-free diagonal
    • I.S. Duff, Algorithm 575, Permutations for a zero-free diagonal, ACM Trans. Math. Software 7 (3) (1981) 387-390.
    • (1981) ACM Trans. Math. Software , vol.7 , Issue.3 , pp. 387-390
    • Duff, I.S.1
  • 11
    • 0019611965 scopus 로고
    • On algorithms for obtaining a maximum transversal
    • I.S. Duff, On algorithms for obtaining a maximum transversal, ACM Trans. Math. Software 7 (3) (1981) 315-330.
    • (1981) ACM Trans. Math. Software , vol.7 , Issue.3 , pp. 315-330
    • Duff, I.S.1
  • 12
    • 0022754738 scopus 로고
    • Parallel implementation of multifrontal schemes
    • I.S. Duff, Parallel implementation of multifrontal schemes, Parallel Computing 3 (1986) 193-204.
    • (1986) Parallel Computing , vol.3 , pp. 193-204
    • Duff, I.S.1
  • 13
    • 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) 302-325.
    • (1983) ACM Trans. Math. Software , vol.9 , pp. 302-325
    • Duff, I.S.1    Reid, J.K.2
  • 18
    • 0025152559 scopus 로고
    • Solving general sparse linear systems using conjugate gradient-type methods
    • Amsterdam, The Netherlands ACM Press, New York
    • K. Gallivan, A. Sameh and Z. Zlatev, Solving general sparse linear systems using conjugate gradient-type methods, in: Proc. 1990 Internat. Conf. on Supercomputing, Amsterdam, The Netherlands (ACM Press, New York, 1990) 132-139.
    • (1990) Proc. 1990 Internat. Conf. on Supercomputing , pp. 132-139
    • Gallivan, K.1    Sameh, A.2    Zlatev, Z.3
  • 19
    • 85031087364 scopus 로고
    • Parallel direct method codes for general sparse matrices
    • Spedicato, Bertocchi and Vespucci, eds.
    • K. Gallivan, A. Sameh and Z. Zlatev, Parallel direct method codes for general sparse matrices, in: Spedicato, Bertocchi and Vespucci, eds., Proc. NATO ASI on Linear Systems, 1991.
    • (1991) Proc. NATO ASI on Linear Systems
    • Gallivan, K.1    Sameh, A.2    Zlatev, Z.3
  • 20
    • 0029209175 scopus 로고    scopus 로고
    • A locally optimized reordering algorithm and its application to a parallel sparse linear system solver
    • K.A. Gallivan, P.C. Hansen, T. Ostromsky and Z. Zlatev, A locally optimized reordering algorithm and its application to a parallel sparse linear system solver, Computing 54 (1) 39-67.
    • Computing , vol.54 , Issue.1 , pp. 39-67
    • Gallivan, K.A.1    Hansen, P.C.2    Ostromsky, T.3    Zlatev, Z.4
  • 22
    • 0007232738 scopus 로고
    • The parallel solution of nonsymmetric sparse linear systems using the H * reordering and an associated factorization
    • Manchester, England
    • K.A. Gallivan, B.A. Marsolf and H.A.G. Wijshoff, The parallel solution of nonsymmetric sparse linear systems using the H * reordering and an associated factorization, in: Proc. 8th ACM Internat. Conf. on Supercomputing Manchester, England (1994) 419-430.
    • (1994) Proc. 8th Acm Internat. Conf. on Supercomputing , pp. 419-430
    • Gallivan, K.A.1    Marsolf, B.A.2    Wijshoff, H.A.G.3
  • 23
    • 30244461628 scopus 로고
    • Tech. Rept. UIUDCS-F-75-885, Department of Computer Science, University of Illinois, Urbana, IL
    • C W. Gear, Numerical errors in sparse linear equations, Tech. Rept. UIUDCS-F-75-885, Department of Computer Science, University of Illinois, Urbana, IL, 1975.
    • (1975) Numerical Errors in Sparse Linear Equations
    • Gear, C.W.1
  • 24
    • 0000264382 scopus 로고
    • Nested dissection of a regular finite element mesh
    • A. George, Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal. 10 (2) (1973) 345-363.
    • (1973) SIAM J. Numer. Anal. , vol.10 , Issue.2 , pp. 345-363
    • George, A.1
  • 25
    • 0000383162 scopus 로고
    • An automatic one-way dissection algorithm for irregular finite element problems
    • A. George, An automatic one-way dissection algorithm for irregular finite element problems, SIAM J. Numer. Anal. 17 (6) (1980) 740-751.
    • (1980) SIAM J. Numer. Anal. , vol.17 , Issue.6 , pp. 740-751
    • George, A.1
  • 26
    • 0000114384 scopus 로고
    • An automatic nested dissection algorithm for irregular finite-element problems
    • A. George and J.W.H. Liu, An automatic nested dissection algorithm for irregular finite-element problems, SIAM J. Numer. Anal. 15 (1978) 1053-1069.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 1053-1069
    • George, A.1    Liu, J.W.H.2
  • 30
    • 0347728943 scopus 로고
    • Finding the block lower triangular form of a matrix
    • J.R. Bunch and D.J. Rose, eds., Academic Press, New York
    • F.G. Gustavson, Finding the block lower triangular form of a matrix, in: J.R. Bunch and D.J. Rose, eds., Sparse Matrix Computations (Academic Press, New York, 1976).
    • (1976) Sparse Matrix Computations
    • Gustavson, F.G.1
  • 32
    • 30244510329 scopus 로고
    • An algorithm for distinct representatives
    • M. Hall Jr, An algorithm for distinct representatives, Amer. Math. Monthly 63 (10) (1956) 716-717.
    • (1956) Amer. Math. Monthly , vol.63 , Issue.10 , pp. 716-717
    • Hall M., Jr.1
  • 34
    • 0001009871 scopus 로고
    • 5/2 algorithm for maximum matchings in bipartite graphs
    • 5/2 algorithm for maximum matchings in bipartite graphs, SIAM J. Comput. 2 (4) (1973) 225-231.
    • (1973) SIAM J. Comput. , vol.2 , Issue.4 , pp. 225-231
    • Hopcroft, J.E.1    Karp, R.M.2
  • 35
    • 0002719797 scopus 로고
    • The Hungarian method for the assignment problem
    • H.W. Kuhn, The Hungarian method for the assignment problem, Naval Research Logistics Quarterly 2 (1) (1955) 83-97.
    • (1955) Naval Research Logistics Quarterly , vol.2 , Issue.1 , pp. 83-97
    • Kuhn, H.W.1
  • 37
    • 30244442683 scopus 로고
    • Hierarchical partition - A new optimal pivoting algorithm
    • T.D. Lin and R.S.H. Mah, Hierarchical partition - A new optimal pivoting algorithm, Mathematical Programming 12:260-278, 1977.
    • (1977) Mathematical Programming , vol.12 , pp. 260-278
    • Lin, T.D.1    Mah, R.S.H.2
  • 39
    • 0026840122 scopus 로고
    • The multifrontal method for sparse matrix solution: Theory and practice
    • J.W.H. Liu, The multifrontal method for sparse matrix solution: Theory and practice, SIAM Review 34 (1) (1992) 82-109.
    • (1992) SIAM Review , vol.34 , Issue.1 , pp. 82-109
    • Liu, J.W.H.1
  • 40
    • 30244490200 scopus 로고
    • Master Thesis, Tech. Rept. CSRD Report No. 1125, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL
    • B. Marsolf, Large grain parallel sparse system solver, Master Thesis, Tech. Rept. CSRD Report No. 1125, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL, 1991.
    • (1991) Large Grain Parallel Sparse System Solver
    • Marsolf, B.1
  • 41
    • 30244439473 scopus 로고
    • An optimization problem arising from tearing methods
    • J.R. Bunch and D.J. Rose, eds., Academic Press, New York
    • A. Sangiovanni-Vincentelli, An optimization problem arising from tearing methods, in: J.R. Bunch and D.J. Rose, eds., Sparse Matrix Computations (Academic Press, New York, 1976) 97-110.
    • (1976) Sparse Matrix Computations , pp. 97-110
    • Sangiovanni-Vincentelli, A.1
  • 42
    • 30244504406 scopus 로고
    • Tech. Rept. CSRD Report No. 1122, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL
    • Staff, The Cedar project, Tech. Rept. CSRD Report No. 1122, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL, 1991.
    • (1991) The Cedar Project
  • 43
    • 0001644344 scopus 로고
    • Partitioning and tearing systems of equations
    • D.V. Steward, Partitioning and tearing systems of equations, SIAM J. Numer. Anal. 2 (2) (1965) 345-365.
    • (1965) SIAM J. Numer. Anal. , vol.2 , Issue.2 , pp. 345-365
    • Steward, D.V.1
  • 44
    • 0001790593 scopus 로고
    • Depth-first search and linear graph algorithms
    • R.E. Tarjan, Depth-first search and linear graph algorithms, SIAM J. Comput. 1 (1972) 146-160.
    • (1972) SIAM J. Comput. , vol.1 , pp. 146-160
    • Tarjan, R.E.1
  • 46
    • 30244487604 scopus 로고    scopus 로고
    • private communication
    • X. Wang, private communication.
    • Wang, X.1
  • 47
    • 0009234991 scopus 로고
    • Tech. Rept. CSRD Report No. 901, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL
    • H.A.G. Wijshoff, Symmetric orderings for unsymmetric sparse matrices, Tech. Rept. CSRD Report No. 901, Center for Supercomputing Research and Development, University of Illinois, Urbana, IL, 1989.
    • (1989) Symmetric Orderings for Unsymmetric Sparse Matrices
    • Wijshoff, H.A.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.