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Volumn 25, Issue 2, 2003, Pages 701-715

Preconditioning sparse nonsymmetric linear systems with the Sherman-Morrison formula

Author keywords

Factorized sparse approximate inverses; Nonsymmetric linear systems; Preconditioned iterative methods; Sherman Morrison formula

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; INVERSE PROBLEMS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; PROBLEM SOLVING;

EID: 2342457098     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502407524     Document Type: Conference Paper
Times cited : (36)

References (25)
  • 1
    • 0001028358 scopus 로고
    • An inverse matrix adjustment arising in discriminant analysis
    • M. S. BARLETT, An inverse matrix adjustment arising in discriminant analysis, Ann. Math. Statist., 22 (1951), pp. 107-111.
    • (1951) Ann. Math. Statist. , vol.22 , pp. 107-111
    • Barlett, M.S.1
  • 3
    • 0034889465 scopus 로고    scopus 로고
    • Robust approximate inverse preconditioning for the conjugate gradient method
    • M. BENZI, J. K. CULLUM, AND M. TŮMA, Robust approximate inverse preconditioning for the conjugate gradient method, SIAM J. Sci. Comput., 22 (2000), pp. 1318-1332.
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 1318-1332
    • Benzi, M.1    Cullum, J.K.2    Tůma, M.3
  • 4
    • 0034884436 scopus 로고    scopus 로고
    • Preconditioning highly indefinite and nonsymmetric matrices
    • M. BENZI, J. C. HAWS, AND M. TŮMA, Preconditioning highly indefinite and nonsymmetric matrices, SIAM J. Sci. Comput., 22 (2000), pp. 1333-1353.
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 1333-1353
    • Benzi, M.1    Haws, J.C.2    Tůma, M.3
  • 5
    • 0035850685 scopus 로고    scopus 로고
    • Stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics
    • M. BENZI, R. KOUHIA, AND M. T?ŮMA, Stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics, Comput. Methods Appl. Mech. Engrg., 190 (2001), pp. 6533-6554.
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 6533-6554
    • Benzi, M.1    Kouhia, R.2    Tůma, M.3
  • 6
    • 0000133360 scopus 로고    scopus 로고
    • A two-level parallel preconditioner based on sparse approximate inverses
    • Iterative Methods in Scientific Computation IV, D. R. Kincaid and A. C. Elster, eds., IMACS, New Brunswick, NJ
    • M. BENZI, J. MARÍN, AND M. TŮMA, A two-level parallel preconditioner based on sparse approximate inverses, in Iterative Methods in Scientific Computation IV, IMACS Ser. Comput. Appl. Math., D. R. Kincaid and A. C. Elster, eds., IMACS, New Brunswick, NJ, 1999, pp. 167-178.
    • (1999) IMACS Ser. Comput. Appl. Math. , pp. 167-178
    • Benzi, M.1    Marín, J.2    Tůma, M.3
  • 7
    • 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
  • 8
    • 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
  • 9
    • 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
  • 10
    • 18844471650 scopus 로고    scopus 로고
    • Orderings for factorized sparse approximate inverse preconditioners
    • M. BENZI AND M. TŮMA, Orderings for factorized sparse approximate inverse preconditioners, SIAM J. Sci. Comput., 21 (2000), pp. 1851-1868.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 1851-1868
    • Benzi, M.1    Tůma, M.2
  • 12
    • 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
  • 13
    • 0029543087 scopus 로고
    • A rank-one reduction formula, and its applications to matrix factorizations
    • M. T. CHU, R. E. FUNDERLIC, AND G. H. GOLUB, A rank-one reduction formula, and its applications to matrix factorizations, SIAM Rev., 37 (1995), pp. 512-530.
    • (1995) SIAM Rev. , vol.37 , pp. 512-530
    • Chu, M.T.1    Funderlic, R.E.2    Golub, G.H.3
  • 14
    • 0012453312 scopus 로고
    • University of Florida sparse matrix collection
    • April 2002
    • T. DAVIS, University of Florida sparse matrix collection, NA Digest, 92 (1994), http://www. cise.ufl.edu/research/sparse/matrices (April 2002).
    • (1994) NA Digest , vol.92
    • Davis, T.1
  • 15
    • 0004109578 scopus 로고
    • User's guide for the Harwell-Boeing sparse matrix collection
    • Rutherford Appleton Laboratory, Chilton, England
    • I. S. DUFF, R. G. GRIMES, AND J. G. LEWIS, User's Guide for the Harwell-Boeing Sparse Matrix Collection, Tech. report RAL-92-886, Rutherford Appleton Laboratory, Chilton, England, 1992.
    • (1992) Tech. Report , vol.RAL-92-886
    • Duff, I.S.1    Grimes, R.G.2    Lewis, J.G.3
  • 17
    • 0031129197 scopus 로고    scopus 로고
    • Parallel preconditioning with sparse approximate inverses
    • M. J. 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.J.1    Huckle, T.2
  • 18
    • 0024682770 scopus 로고
    • Updating the inverse of a matrix
    • W. W. HAGER, Updating the inverse of a matrix, SIAM Rev., 31 (1989), pp. 221-239.
    • (1989) SIAM Rev. , vol.31 , pp. 221-239
    • Hager, W.W.1
  • 20
    • 84966225158 scopus 로고
    • An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
    • J. A. MEUERINK AND H. A. VAN DER VORST, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comp., 31 (1977), pp. 148-162.
    • (1977) Math. Comp. , vol.31 , pp. 148-162
    • Meuerink, J.A.1    Van Der Vorst, H.A.2
  • 22
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869.
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 23
    • 0000905617 scopus 로고
    • Adjustment of an inverse matrix, corresponding to a change in one element of a given matrix
    • J. SHERMAN AND W. MORRISON, Adjustment of an inverse matrix, corresponding to a change in one element of a given matrix, Ann. Math. Statist., 21 (1950), pp. 124-127.
    • (1950) Ann. Math. Statist. , vol.21 , pp. 124-127
    • Sherman, J.1    Morrison, W.2
  • 24
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems
    • H. A. VAN DER VORST, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13 (1992), pp. 631-644.
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1
  • 25
    • 2342573082 scopus 로고
    • Matrix inversion by the annihilation of rank
    • H. S. WILF, Matrix inversion by the annihilation of rank, J. Soc. Indust. Appl. Math., 7 (1959), pp. 149-151.
    • (1959) J. Soc. Indust. Appl. Math. , vol.7 , pp. 149-151
    • Wilf, H.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.