메뉴 건너뛰기




Volumn 2, Issue 2, 2005, Pages 147-161

A variable preconditioning using the sor method for GCR-like methods

Author keywords

Generalized conjugate residual method; Generalized minimal residual method; Inner loop and outerloop; Linear systems; Variable preconditioning

Indexed keywords


EID: 85009741548     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (26)

References (21)
  • 1
    • 34250098040 scopus 로고
    • A Generalized Conjugate Gradient, Least Square Method
    • O. Axelsson, A Generalized Conjugate Gradient, Least Square Method, Numer. Math., 51 (1987) 209-227.
    • (1987) Numer. Math. , vol.51 , pp. 209-227
    • Axelsson, O.1
  • 2
    • 0001116752 scopus 로고
    • A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable-step Preconditioning
    • O. Axelsson and P. S. Vassilevski, A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable-step Preconditioning, SIAM J. Numer. Anal., 12 (1991) 625-644.
    • (1991) SIAM J. Numer. Anal. , vol.12 , pp. 625-644
    • Axelsson, O.1    Vassilevski, P.S.2
  • 3
    • 0001350531 scopus 로고
    • An Iterative Method for the Helmholtz Equations
    • A. Bayliss, C. Goldstein and E. Turkel, An Iterative Method for the Helmholtz Equations, J. Compu. Phys., 49 (1983) 443-457.
    • (1983) J. Compu. Phys. , vol.49 , pp. 443-457
    • Bayliss, A.1    Goldstein, C.2    Turkel, E.3
  • 5
    • 0000011239 scopus 로고
    • Variational Iterative Methods for Nonsym-metric Systems of Linear Equations
    • S. C. Eisenstat, H. C. Elman and M. H. Schultz, Variational Iterative Methods for Nonsym-metric Systems of Linear Equations, SIAM J. Numer. Anal., 20 (1983) 345-357.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 345-357
    • Eisenstat, S.C.1    Elman, H.C.2    Schultz, M.H.3
  • 7
    • 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) 315-339.
    • (1991) Numer. Math. , vol.60 , pp. 315-339
    • Freund, R.W.1    Nachtigal, N.M.2
  • 8
    • 0004236492 scopus 로고    scopus 로고
    • Third ed., The Johns Hopkins University Press, Baltimore and London
    • H. G. Golub and F. C. van Loan, Matrix Computations, Third ed., The Johns Hopkins University Press, Baltimore and London, 1996.
    • (1996) Matrix Computations
    • Golub, H.G.1    Van Loan, F.C.2
  • 9
    • 0033293064 scopus 로고    scopus 로고
    • Inexact Preconditioned Conjugate Gradient Method with Inner-Outer Iteration
    • H. G. Golub and Q. Ye, Inexact Preconditioned Conjugate Gradient Method with Inner-Outer Iteration, SIAM J. Sci. Comput., 21 (1999) 1305-1320.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 1305-1320
    • Golub, H.G.1    Ye, Q.2
  • 10
    • 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. Bur. Standards, 49 (1952) 409-435.
    • (1952) J. Res. Nat. Bur. Standards , vol.49 , pp. 409-435
    • Hestenes, M.R.1    Stiefel, E.2
  • 11
    • 0000090638 scopus 로고
    • Lanczos Methods for the Solution of Nonsymmetric Systems of Linear Equa-tions
    • W. D. Joubert, Lanczos Methods for the Solution of Nonsymmetric Systems of Linear Equa-tions, SIAM J. Matrix Anal. Appl., 13 (1992) 926-943.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 926-943
    • Joubert, W.D.1
  • 12
    • 84966225158 scopus 로고
    • An Iterative Solution Method for Linear Systems of which the Coe±cient 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 Coe±cient Matrix is a Symmetric M-matrix, Math. Comp., 31 (1977) 148-162.
    • (1977) Math. Comp. , vol.31 , pp. 148-162
    • Meijerink, J.A.1    Van der Vorst, H.A.2
  • 13
    • 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) 856-869.
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 14
    • 0242524326 scopus 로고    scopus 로고
    • Iterative Methods for Sparse Linear Systems
    • Y. Saad, Iterative Methods for Sparse Linear Systems, PWS, Boston, 1996.
    • (1996) PWS, Boston
    • Saad, Y.1
  • 15
    • 0000954680 scopus 로고
    • A Flexible Inner-outer Preconditioned GMRES Algorithm
    • Y. Saad, A Flexible Inner-outer Preconditioned GMRES Algorithm, SIAM J. Sci. Stat. Com-put., 14 (1993) 461-469.
    • (1993) SIAM J. Sci. Stat. Com-put. , vol.14 , pp. 461-469
    • Saad, Y.1
  • 16
    • 0036229185 scopus 로고    scopus 로고
    • FQMR: A Flexible Quasi-Minimal Residual Method with Inexact Preconditioning
    • D. B. Szyld and J. A. Yogel, FQMR: A Flexible Quasi-Minimal Residual Method with Inexact Preconditioning, SIAM J. Sci. Stat. Comput., 23 (2001) 363-380.
    • (2001) SIAM J. Sci. Stat. Comput. , vol.23 , pp. 363-380
    • Szyld, D.B.1    Yogel, J.A.2
  • 17
    • 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) 631-644.
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 631-644
    • van der Vorst, H.A.1
  • 19
    • 0003943048 scopus 로고    scopus 로고
    • 2nd rev. and expanded ed., Springer-Verlag, Berlin, Heidelberg, New York
    • R. Varga, Matrix Iterative Analysis, 2nd rev. and expanded ed., Springer-Verlag, Berlin, Heidelberg, New York, 2000.
    • (2000) Matrix Iterative Analysis
    • Varga, R.1
  • 20
    • 0016873451 scopus 로고
    • Orthomin, An Iterative Method for Solving Sparse Sets of Simultaneous Linear Equations
    • Society of Petroleum Engineers of AIME
    • P. K. W. Vinsom, Orthomin, An Iterative Method for Solving Sparse Sets of Simultaneous Linear Equations, in: Proc. Fourth Symposium on Reservoir Simulation, p.149-159, Society of Petroleum Engineers of AIME, 1976.
    • (1976) Proc. Fourth Symposium on Reservoir Simulation , pp. 149-159
    • Vinsom, P.K.W.1
  • 21
    • 0027558806 scopus 로고
    • Solution of the Discretized Incompressible Navier-Stokes Equations with the GMRES Method
    • C. Vuik, Solution of the Discretized Incompressible Navier-Stokes Equations with the GMRES Method, Int. J. for Num. Meth. in Fluids, 16 (1993) 507-523.
    • (1993) Int. J. for Num. Meth. in Fluids , vol.16 , pp. 507-523
    • Vuik, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.