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Volumn 41, Issue 1, 2001, Pages 53-70

A class of incomplete orthogonal factorization methods. I: Methods and theories

Author keywords

Givens rotations; Incomplete orthogonal factorizations; Linear systems; Modified Gram Schmidt orthogonalization; Preconditioning; Sparse least squares

Indexed keywords


EID: 0042275964     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021913700691     Document Type: Article
Times cited : (48)

References (19)
  • 3
    • 0001249888 scopus 로고
    • Block preconditioning for the conjugate gradient method
    • P. Concus, G. H. Golub, and G. Meurant, Block preconditioning for the conjugate gradient method, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 220-252.
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 220-252
    • Concus, P.1    Golub, G.H.2    Meurant, G.3
  • 4
    • 84966217951 scopus 로고
    • Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization
    • J. Daniel, W. B. Gragg, L. Kaufman, and G. W. Stewart, Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comp., 30 (1976), pp. 772-95.
    • (1976) Math. Comp. , vol.30 , pp. 772-795
    • Daniel, J.1    Gragg, W.B.2    Kaufman, L.3    Stewart, G.W.4
  • 5
    • 0042582037 scopus 로고
    • Fourier analysis of incomplete factorization preconditioners for three dimensional anisotropic problems
    • J. M. Donato and T. F. Chan, Fourier analysis of incomplete factorization preconditioners for three dimensional anisotropic problems, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 319-338.
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 319-338
    • Donato, J.M.1    Chan, T.F.2
  • 6
    • 84966211825 scopus 로고
    • A stability analysis of incomplete LU factorizations
    • H. C. Elman, A stability analysis of incomplete LU factorizations, Math. Comp., 47 (1986), pp. 191-217.
    • (1986) Math. Comp. , vol.47 , pp. 191-217
    • Elman, H.C.1
  • 7
    • 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
  • 8
    • 0002149257 scopus 로고
    • Solution of sparse linear least squares problems using Givens rotations
    • A. George and M. T. Heath, Solution of sparse linear least squares problems using Givens rotations, Linear Alg. Appl., 34 (1980), pp. 69-83.
    • (1980) Linear Alg. Appl. , vol.34 , pp. 69-83
    • George, A.1    Heath, M.T.2
  • 9
    • 0000687288 scopus 로고
    • On the complexity of sparse QR and LU factorisation of finite element matrices
    • A. George and E. Ng, On the complexity of sparse QR and LU factorisation of finite element matrices, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 849-861.
    • (1988) SIAM J. Sci. Statist. Comput. , vol.9 , pp. 849-861
    • George, A.1    Ng, E.2
  • 10
    • 0039506156 scopus 로고    scopus 로고
    • Separators and structure prediction in sparse orthogonal factorisation
    • J. R. Gilbert, E. Ng, and W. Peyton, Separators and structure prediction in sparse orthogonal factorisation, Linear Alg. Appl., 262 (1997), pp. 83-97.
    • (1997) Linear Alg. Appl. , vol.262 , pp. 83-97
    • Gilbert, J.R.1    Ng, E.2    Peyton, W.3
  • 11
    • 0003039594 scopus 로고
    • A class of first order factorizations
    • I. Gustafsson, A class of first order factorizations, BIT, 18 (1978), pp. 142-156.
    • (1978) BIT , vol.18 , pp. 142-156
    • Gustafsson, I.1
  • 12
    • 0008402128 scopus 로고
    • Incomplete methods for solving A′Ax = b
    • A. Jennings and M. A. Ajiz, Incomplete methods for solving A′Ax = b, SIAM J. Sci. Statist. Comput., 5:4 (1984), pp. 978-987.
    • (1984) SIAM J. Sci. Statist. Comput. , vol.5 , Issue.4 , pp. 978-987
    • Jennings, A.1    Ajiz, M.A.2
  • 13
    • 84966241510 scopus 로고
    • An incomplete factorization technique for positive definite linear systems
    • T. A. Manteuffel, An incomplete factorization technique for positive definite linear systems, Math. Comp., 34 (1980), pp. 473-497.
    • (1980) Math. Comp. , vol.34 , pp. 473-497
    • Manteuffel, T.A.1
  • 14
    • 84966225158 scopus 로고
    • An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix
    • J. A. Meijerink 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
    • Meijerink, J.A.1    Van Der Vorst, H.A.2
  • 15
    • 0002598644 scopus 로고
    • Preconditioning techniques for nonsymmetric and indefinite linear systems
    • Y. Saad, Preconditioning techniques for nonsymmetric and indefinite linear systems, J. Comput. Appl. Math., 24 (1988), pp. 89-105.
    • (1988) J. Comput. Appl. Math. , vol.24 , pp. 89-105
    • Saad, Y.1
  • 16
    • 84985408358 scopus 로고
    • ILUT: A dual threshold incomplete ILU factorization
    • Y. Saad, ILUT: A dual threshold incomplete ILU factorization, Numer. Linear Algebra Appl., 1 (1994), pp. 387-402.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 387-402
    • Saad, Y.1
  • 18
    • 0031082735 scopus 로고    scopus 로고
    • CIMGS: A incomplete orthogonalization preconditioner
    • X. Wang, K. A. Gallivan, and R. Bramley, CIMGS: A incomplete orthogonalization preconditioner, SIAM J. Sci. Comput., 18 (1997), pp. 516-536.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 516-536
    • Wang, X.1    Gallivan, K.A.2    Bramley, R.3
  • 19
    • 0013356388 scopus 로고
    • Comparison of two pivotal strategies in sparse plane rotations
    • Z. Zlatev, Comparison of two pivotal strategies in sparse plane rotations, Internat. J. Comput. Appl., 8 (1982), pp. 119-135.
    • (1982) Internat. J. Comput. Appl. , vol.8 , pp. 119-135
    • Zlatev, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.