메뉴 건너뛰기




Volumn 25, Issue 1-4, 2000, Pages 1-22

On the sublinear and superlinear rate of convergence of conjugate gradient methods

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034560792     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1016694031362     Document Type: Article
Times cited : (33)

References (22)
  • 2
    • 0017009452 scopus 로고
    • A class of iterative methods for finite element equations
    • O. Axelsson, A class of iterative methods for finite element equations, Comput. Methods Appl. Mech. Engrg. 9 (1976) 123-137.
    • (1976) Comput. Methods Appl. Mech. Engrg. , vol.9 , pp. 123-137
    • Axelsson, O.1
  • 3
    • 0024281733 scopus 로고
    • A restarted version of a generalized preconditioned conjugate gradient method
    • O. Axelsson, A restarted version of a generalized preconditioned conjugate gradient method, Commun. Appl. Numer. Methods 4 (1988) 521-530.
    • (1988) Commun. Appl. Numer. Methods , vol.4 , pp. 521-530
    • Axelsson, O.1
  • 4
    • 0002335196 scopus 로고
    • Bounds of eigenvalues of preconditioned matrices
    • O. Axelsson, Bounds of eigenvalues of preconditioned matrices, SIAM J. Matrix Anal. 13 (1992) 847-862.
    • (1992) SIAM J. Matrix Anal. , vol.13 , pp. 847-862
    • Axelsson, O.1
  • 6
    • 0003847853 scopus 로고
    • Condition numbers for the study of the rate of convergence of the conjugate gradient method
    • Blagoevgrad, Bulgaria, 17-20 June
    • O. Axelsson, Condition numbers for the study of the rate of convergence of the conjugate gradient method, in: Proc. of the 2nd IMACS Internat. Symposium on Iterative Methods in Linear Algebra, Blagoevgrad, Bulgaria, 17-20 June 1995, pp. 3-33.
    • (1995) Proc. of the 2nd IMACS Internat. Symposium on Iterative Methods in Linear Algebra , pp. 3-33
    • Axelsson, O.1
  • 8
    • 0000696639 scopus 로고
    • On the rate of convergence of the preconditioned conjugate gradient method
    • O. Axelsson and G. Lindskog, On the rate of convergence of the preconditioned conjugate gradient method, Numer. Math. 48 (1986) 499-523.
    • (1986) Numer. Math. , vol.48 , pp. 499-523
    • Axelsson, O.1    Lindskog, G.2
  • 9
    • 0042606432 scopus 로고
    • The bordering method as a preconditioning method
    • Vestnik Moscow University Ser. 15
    • O. Axelsson, M. Neytcheva and B. Polman, The bordering method as a preconditioning method, Vestnik Moscow University Ser. 15, Vychisl. Math. Cybernet. (1995) 3-24.
    • (1995) Vychisl. Math. Cybernet , pp. 3-24
    • Axelsson, O.1    Neytcheva, M.2    Polman, B.3
  • 10
    • 0042105330 scopus 로고    scopus 로고
    • A generalized conjugate gradient minimum residual method (GCG-MR) with variable preconditioners and a relation between residuals of the GCG-MR and GCG-OR methods
    • O. Axelsson and M. Nikolova, A generalized conjugate gradient minimum residual method (GCG-MR) with variable preconditioners and a relation between residuals of the GCG-MR and GCG-OR methods, Commun. Appl. Anal. 1(3) (1997) 371-388.
    • (1997) Commun. Appl. Anal. , vol.1 , Issue.3 , pp. 371-388
    • Axelsson, O.1    Nikolova, M.2
  • 11
    • 0001355114 scopus 로고
    • Comparison of splittings used with the conjugate gradient algorithm
    • A. Greenbaum, Comparison of splittings used with the conjugate gradient algorithm, Numer. Math. 33 (1979) 181-194.
    • (1979) Numer. Math. , vol.33 , pp. 181-194
    • Greenbaum, A.1
  • 12
    • 0000002780 scopus 로고
    • Predicting the behaviour of finite precision Lanczos and conjugate gradient computations
    • A. Greenbaum and Z. Strakos, Predicting the behaviour of finite precision Lanczos and conjugate gradient computations, SIAM J. Matrix Anal. Appl. 13 (1992) 121-137.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 121-137
    • Greenbaum, A.1    Strakos, Z.2
  • 13
    • 0010007548 scopus 로고
    • Iterative methods for solving linear problems in Hilbert spaces
    • Contributions to the Solutions of Systems of Linear Equations and the Determination of Eigenvalues, ed. O. Tausky, Washington, DC
    • R.M. Hayes, Iterative methods for solving linear problems in Hilbert spaces, in: Contributions to the Solutions of Systems of Linear Equations and the Determination of Eigenvalues, ed. O. Tausky, Nat. Bur. Standards Appl. Math. Ser., Vol. 39 (Washington, DC, 1954) pp. 71-103.
    • (1954) Nat. Bur. Standards Appl. Math. Ser. , vol.39 , pp. 71-103
    • Hayes, R.M.1
  • 14
    • 0002716202 scopus 로고
    • Influence of the eigenvalue spectrum on the convergence rate of the conjugate gradient method
    • A. Jennings, Influence of the eigenvalue spectrum on the convergence rate of the conjugate gradient method, J. Inst. Math. Appl. 20 (1977) 61-72.
    • (1977) J. Inst. Math. Appl. , vol.20 , pp. 61-72
    • Jennings, A.1
  • 15
    • 0007201659 scopus 로고
    • Two-level explicit preconditionings for the conjugate gradient method
    • I.E. Kaporin, Two-level explicit preconditionings for the conjugate gradient method, Differential Equations 28 (1992) 280-289.
    • (1992) Differential Equations , vol.28 , pp. 280-289
    • Kaporin, I.E.1
  • 16
    • 84985376638 scopus 로고
    • New convergence results and preconditioning strategies for the conjugate gradient method
    • I.E. Kaporin, New convergence results and preconditioning strategies for the conjugate gradient method, Numer. Linear Algebra Appl. 1 (1994) 179-210.
    • (1994) Numer. Linear Algebra Appl. , vol.1 , pp. 179-210
    • Kaporin, I.E.1
  • 18
    • 0003778131 scopus 로고
    • Convergence of Iterations for Linear Equations
    • ETH Zürich Birkhäuser, Basel
    • O. Nevanlinna, Convergence of Iterations for Linear Equations, Lectures in Mathematics, ETH Zürich (Birkhäuser, Basel, 1993).
    • (1993) Lectures in Mathematics
    • Nevanlinna, O.1
  • 19
    • 21144467170 scopus 로고
    • On the convergence rate of the conjugate gradients in presence of rounding errors
    • Y. Notay, On the convergence rate of the conjugate gradients in presence of rounding errors, Numer. Math. 65 (1993) 301-317.
    • (1993) Numer. Math. , vol.65 , pp. 301-317
    • Notay, Y.1
  • 20
    • 0001403122 scopus 로고
    • The rate of convergence of conjugate gradients
    • A. van der Sluis and H.A. van der Vorst, The rate of convergence of conjugate gradients, Numer. Math. 48 (1986) 543-560.
    • (1986) Numer. Math. , vol.48 , pp. 543-560
    • Van Der Sluis, A.1    Van Der Vorst, H.A.2
  • 21
    • 0000469387 scopus 로고
    • The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors
    • Preconditioned Conjugate Gradient Methods, eds. O. Axelsson and L.Yu. Kolotilina, Springer Berlin
    • H.A. van der Vorst, The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors, in: Preconditioned Conjugate Gradient Methods, eds. O. Axelsson and L.Yu. Kolotilina, Lecture Notes in Mathematics, Vol. 1457 (Springer Berlin, 1989) pp. 126-136.
    • (1989) Lecture Notes in Mathematics , vol.1457 , pp. 126-136
    • Van Der Vorst, H.A.1
  • 22
    • 0000570696 scopus 로고
    • Iterative methods by space decomposition and subspace correction
    • J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Rev. 24 (1992) 581-613.
    • (1992) SIAM Rev. , vol.24 , pp. 581-613
    • Xu, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.