메뉴 건너뛰기




Volumn 44, Issue 1, 2004, Pages 189-207

Semi-conjugate direction methods for real positive definite systems

Author keywords

Conjugate gradient method; Gaussian elimination; Left conjugate direction method; Left conjugate direction vectors; LU decomposition; Right conjugate direction vectors; Semi conjugate direction method; Solution of nonsymmetric linear systems

Indexed keywords


EID: 3142527273     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:BITN.0000025092.92213.da     Document Type: Article
Times cited : (18)

References (16)
  • 1
    • 0002205748 scopus 로고
    • Conjugate gradient type methods for nonsymmetric and inconsistent systems of linear equations
    • O. Axelsson, Conjugate gradient type methods for nonsymmetric and inconsistent systems of linear equations, Linear Algebra Appl., 29 (1980), pp. 1-16.
    • (1980) Linear Algebra Appl. , vol.29 , pp. 1-16
    • Axelsson, O.1
  • 2
    • 0026104373 scopus 로고
    • The nonsymmetric Lanczos algorithm and controllability
    • D. L. Boley and G. H. Golub, The nonsymmetric Lanczos algorithm and controllability, Systems Control Lett., 16 (1991), pp. 97-105.
    • (1991) Systems Control Lett. , vol.16 , pp. 97-105
    • Boley, D.L.1    Golub, G.H.2
  • 3
    • 21344496401 scopus 로고
    • Adaptive Chebyshev iterative methods for nonsymmetric linear systems based on modified moments
    • D. Calvetti, G. H. Golub, and L. Reichel, Adaptive Chebyshev iterative methods for nonsymmetric linear systems based on modified moments, Numer. Math., 67 (1994), pp. 21-40.
    • (1994) Numer. Math. , vol.67 , pp. 21-40
    • Calvetti, D.1    Golub, G.H.2    Reichel, L.3
  • 5
    • 0002576532 scopus 로고
    • A generalized conjugate gradient method for nonsymmetric systems of linear equations
    • R. Glowinski and J. L. Lions, eds., Lecture Notes in Economics and Mathematical Systems 134, Springer, Berlin
    • P. Concus and G. H. Golub, A generalized conjugate gradient method for nonsymmetric systems of linear equations, in Computing Methods in Applied Sciences and Engineering, R. Glowinski and J. L. Lions, eds., Lecture Notes in Economics and Mathematical Systems 134, Springer, Berlin, 1976, pp. 56-65.
    • (1976) Computing Methods in Applied Sciences and Engineering , pp. 56-65
    • Concus, P.1    Golub, G.H.2
  • 6
    • 4043106140 scopus 로고    scopus 로고
    • Private communication, April
    • Y.-H. Dai, Private communication, April, 1999.
    • (1999)
    • Dai, Y.-H.1
  • 7
    • 3142570750 scopus 로고    scopus 로고
    • Study on semi-conjugate direction methods for nonsymmetric systems
    • to appear
    • Y.-H. Dai and J. Y. Yuan, Study on semi-conjugate direction methods for nonsymmetric systems, Internat. J. Numer. Methods Engrg. 60 (2004) (to appear).
    • (2004) Internat. J. Numer. Methods Engrg. , vol.60
    • Dai, Y.-H.1    Yuan, J.Y.2
  • 8
    • 0021416130 scopus 로고
    • Necessary and sufficient conditions for the existence of a conjugate gradient method
    • V. Faber and T. Manteuffel, Necessary and sufficient conditions for the existence of a conjugate gradient method, SIAM J. Numer. Anal., 21 (1984), pp. 352-362.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 352-362
    • Faber, V.1    Manteuffel, T.2
  • 10
    • 25444452938 scopus 로고
    • QMR: A quasi-minimal residual method for non-Hermitian linear systems
    • R. W. Freund and N. M. Nachtigal, QMR: A quasi-minimal residual method for non-Hermitian linear systems, Numer. Math., 60 (1991), pp. 315-339.
    • (1991) Numer. Math. , vol.60 , pp. 315-339
    • Freund, R.W.1    Nachtigal, N.M.2
  • 11
    • 84968452648 scopus 로고
    • Iterative solution of linear systems
    • Cambridge University Press
    • R. W. Freund, G. H. Golub, and N. M. Nachtigal, Iterative Solution of Linear Systems, in Acta Numerica, Cambridge University Press, 1992, pp. 57-100.
    • (1992) Acta Numerica , pp. 57-100
    • Freund, R.W.1    Golub, G.H.2    Nachtigal, N.M.3
  • 12
    • 0000135303 scopus 로고
    • Methods of conjugate gradients for solving linear systems
    • M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bureau of Standards, B49 (1952), pp. 409-436.
    • (1952) J. Res. Nat. Bureau of Standards , vol.B49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 13
    • 84966222159 scopus 로고
    • Krylov subspace methods for solving large unsymmetric linear systems
    • Y. Saad, Krylov subspace methods for solving large unsymmetric linear systems, Math. Comput., 37 (1981), pp. 105-126.
    • (1981) Math. Comput. , vol.37 , pp. 105-126
    • Saad, Y.1
  • 14
    • 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
  • 16
    • 34250433174 scopus 로고
    • Conjugate direction methods for solving systems of linear equations
    • G. W. Stewart, Conjugate direction methods for solving systems of linear equations, Numer. Math., 21 (1973), pp. 285-297.
    • (1973) Numer. Math. , vol.21 , pp. 285-297
    • Stewart, G.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.