메뉴 건너뛰기




Volumn 21, Issue 5, 2000, Pages 1851-1868

Orderings for factorized sparse approximate inverse preconditioners

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; HEURISTIC METHODS; INVERSE PROBLEMS; MATRIX ALGEBRA; VECTORS;

EID: 18844471650     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827598339372     Document Type: Article
Times cited : (68)

References (38)
  • 2
    • 0004675411 scopus 로고    scopus 로고
    • A sparse approximate inverse preconditioner for the conjugate gradient method
    • M. BENZI, C. D. MEYER, AND M. TŮMA, A sparse approximate inverse preconditioner for the conjugate gradient method, SIAM J. Sci. Comput., 17 (1996), pp. 1135-1149.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 1135-1149
    • Benzi, M.1    Meyer, C.D.2    Tůma, M.3
  • 3
    • 0033293791 scopus 로고    scopus 로고
    • Orderings for incomplete factorization preconditioning of nonsymmetric problems
    • M. BENZI, D. B. SZYLD, AND A. VAN DUIN, Orderings for incomplete factorization preconditioning of nonsymmetric problems, SIAM J. Sci. Comput., 20 (1999), pp. 1652-1670.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1652-1670
    • Benzi, M.1    Szyld, D.B.2    Van Duin, A.3
  • 4
    • 0001135947 scopus 로고    scopus 로고
    • A sparse approximate inverse preconditioner for nonsymmetric linear systems
    • M. BENZI AND M. TŮMA, A sparse approximate inverse preconditioner for nonsymmetric linear systems, SIAM J. Sci. Comput., 19 (1998), pp. 968-994.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 968-994
    • Benzi, M.1    Tůma, M.2
  • 5
    • 0001635061 scopus 로고    scopus 로고
    • Numerical experiments with two approximate inverse preconditioners
    • M. BENZI AND M. TŮMA, Numerical experiments with two approximate inverse preconditioners, BIT, 38 (1998), pp. 234-241.
    • (1998) BIT , vol.38 , pp. 234-241
    • Benzi, M.1    Tůma, M.2
  • 6
    • 0033149240 scopus 로고    scopus 로고
    • A comparative study of sparse approximate inverse preconditioners
    • M. BENZI AND M. TŮMA, A comparative study of sparse approximate inverse preconditioners, Appl. Numer. Math., 30 (1999), pp. 305-340.
    • (1999) Appl. Numer. Math. , vol.30 , pp. 305-340
    • Benzi, M.1    Tůma, M.2
  • 7
    • 0033295138 scopus 로고    scopus 로고
    • Ordering, anisotropy and factored sparse approximate inverses
    • R. BRIDSON AND W.-P. TANG, Ordering, anisotropy and factored sparse approximate inverses, SIAM J. Sci. Comput., 21 (1999), pp. 867-882.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 867-882
    • Bridson, R.1    Tang, W.-P.2
  • 8
    • 0001238648 scopus 로고    scopus 로고
    • Wavelet sparse approximate inverse preconditioners
    • T. CHAN, W.-P. TANG, AND W. WAN, Wavelet sparse approximate inverse preconditioners, BIT, 37 (1997), pp. 644-660.
    • (1997) BIT , vol.37 , pp. 644-660
    • Chan, T.1    Tang, W.-P.2    Wan, W.3
  • 9
    • 0001630026 scopus 로고    scopus 로고
    • Approximate inverse preconditioners via sparse-sparse iterations
    • E. CHOW AND Y. SAAD, Approximate inverse preconditioners via sparse-sparse iterations, SIAM J. Sci. Comput., 19 (1998), pp. 995-1023.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 995-1023
    • Chow, E.1    Saad, Y.2
  • 10
    • 0013269731 scopus 로고
    • University of Florida sparse matrix collection
    • October
    • T. DAVIS, University of Florida Sparse Matrix Collection, NA Digest, vol. 94, issue 42, October 1994; also available online from http://www.cise.ufl.edu/∼davis/sparse/.
    • (1994) NA Digest , vol.94 , Issue.42
    • Davis, T.1
  • 11
    • 84966252352 scopus 로고
    • Decay rates for inverses of band matrices
    • S. DEMKO, W. F. MOSS, AND P. W. SMITH, Decay rates for inverses of band matrices, Math. Comp., 43 (1984), pp. 491-499.
    • (1984) Math. Comp. , vol.43 , pp. 491-499
    • Demko, S.1    Moss, W.F.2    Smith, P.W.3
  • 14
    • 0000602242 scopus 로고
    • The effect of ordering on preconditioned conjugate gradients
    • I. S. DUFF AND G. A. MEURANT, The effect of ordering on preconditioned conjugate gradients, BIT, 29 (1989), pp. 635-657.
    • (1989) BIT , vol.29 , pp. 635-657
    • Duff, I.S.1    Meurant, G.A.2
  • 15
    • 38249027025 scopus 로고
    • Decay rates of inverses of banded M-matrices that are near to Toeplitz matrices
    • V. EIJKHOUT AND B. POLMAN, Decay rates of inverses of banded M-matrices that are near to Toeplitz matrices, Linear Algebra Appl., 109 (1988), pp. 247-277.
    • (1988) Linear Algebra Appl. , vol.109 , pp. 247-277
    • Eijkhout, V.1    Polman, B.2
  • 16
    • 0001330133 scopus 로고
    • Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems
    • H. C. ELMAN, Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems, BIT, 29 (1989), pp. 890-915.
    • (1989) BIT , vol.29 , pp. 890-915
    • Elman, H.C.1
  • 17
    • 0003423573 scopus 로고    scopus 로고
    • Improving the performance of factorised sparse approximate inverse preconditioner
    • Dublin, Ireland
    • M. R. FIELD, Improving the Performance of Factorised Sparse Approximate Inverse Preconditioner, Hitachi Dublin Laboratory Technical Report HDL-TR-98-199, Dublin, Ireland, 1998.
    • (1998) Hitachi Dublin Laboratory Technical Report HDL-TR-98-199
    • Field, M.R.1
  • 19
    • 21344476775 scopus 로고
    • Predicting structure in sparse matrix computations
    • J. R. GILBERT, Predicting structure in sparse matrix computations, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 62-79.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 62-79
    • Gilbert, J.R.1
  • 20
    • 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
  • 22
    • 0031129197 scopus 로고    scopus 로고
    • Parallel preconditioning with sparse approximate inverses
    • M. GROTE AND T. HUCKLE, Parallel preconditioning with sparse approximate inverses, SIAM J. Sci. Comput., 18 (1997), pp. 838-853.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 838-853
    • Grote, M.1    Huckle, T.2
  • 25
    • 21144474663 scopus 로고
    • Factorized sparse approximate inverse preconditioning I: Theory
    • L. YU. KOLOTILINA AND A. YU. YEREMIN, Factorized sparse approximate inverse preconditioning I: Theory, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 45-58.
    • (1993) SIAM J. Matrix Anal. Appl. , vol.14 , pp. 45-58
    • Kolotilina, L.Yu.1    Yeremin, A.Yu.2
  • 26
    • 0000421739 scopus 로고
    • A fast algorithm for reordering sparse matrices for parallel factorization
    • J. G. LEWIS, B. W. PEYTON, AND A. POTHEN, A fast algorithm for reordering sparse matrices for parallel factorization, SIAM J. Sci. Statist. Comput., 10 (1989), pp. 1156-1173.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 1156-1173
    • Lewis, J.G.1    Peyton, B.W.2    Pothen, A.3
  • 28
    • 0022077450 scopus 로고
    • Modification of the minimum degree algorithm by multiple elimination
    • J. W. H. LIU, Modification of the minimum degree algorithm by multiple elimination, ACM Trans. Math. Software, 11 (1985), pp. 141-153.
    • (1985) ACM Trans. Math. Software , vol.11 , pp. 141-153
    • Liu, J.W.H.1
  • 29
    • 0004445856 scopus 로고
    • Equivalent sparse matrix reordering by elimination tree rotations
    • J. W. H. LIU, Equivalent sparse matrix reordering by elimination tree rotations, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 424-444.
    • (1988) SIAM J. Sci. Statist. Comput. , vol.9 , pp. 424-444
    • Liu, J.W.H.1
  • 30
    • 0024698976 scopus 로고
    • Reordering sparse matrices for parallel elimination
    • J. W. H. LIU, Reordering sparse matrices for parallel elimination, Parallel Comput., 11 (1989), pp. 73-91.
    • (1989) Parallel Comput. , vol.11 , pp. 73-91
    • Liu, J.W.H.1
  • 32
    • 0000809242 scopus 로고
    • A review of the inverse of symmetric tridiagonal and block tridiagonal matrices
    • G. MEURANT, A review of the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 707-728.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 707-728
    • Meurant, G.1
  • 33
    • 85037792386 scopus 로고    scopus 로고
    • private communication, December
    • G. MEURANT, private communication, December 1997.
    • (1997)
    • Meurant, G.1
  • 34
    • 0033239810 scopus 로고    scopus 로고
    • Decay rates of the inverse of nonsymmetric tridiagonal and band matrices
    • R. NABBEN, Decay rates of the inverse of nonsymmetric tridiagonal and band matrices, SIAM J. Matrix Anal. Appl., 20 (1999), pp. 820-837.
    • (1999) SIAM J. Matrix Anal. Appl. , vol.20 , pp. 820-837
    • Nabben, R.1
  • 35
    • 0004056810 scopus 로고
    • Technical Report CS-88-13, Pennsylvania State University, University Park, PA
    • A. POTHEN, The Complexity of Optimal Elimination Trees, Technical Report CS-88-13, Pennsylvania State University, University Park, PA, 1988.
    • (1988) The Complexity of Optimal Elimination Trees
    • Pothen, A.1
  • 38
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems
    • H. A. VAN DER VORST, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems, SIAM J. Sci. Statist. Comput., 12 (1992), pp. 631-644.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 631-644
    • Van Der Vorst, H.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.