메뉴 건너뛰기




Volumn 21, Issue 4, 2000, Pages 1279-1299

An augmented conjugate gradient method for solving consecutive symmetric positive definite linear systems

Author keywords

Conjugate gradient; Krylov subspace; Orthogonal projection

Indexed keywords


EID: 0034144760     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479897330194     Document Type: Article
Times cited : (63)

References (30)
  • 3
    • 0032343927 scopus 로고    scopus 로고
    • Augmented conjugate gradient. Application in an iterative process for the solution of scattering problems
    • M.-O. BRISTEAU AND J. ERHEL, Augmented conjugate gradient. Application in an iterative process for the solution of scattering problems, Numer. Algorithms, 18 (1998), pp. 71-90.
    • (1998) Numer. Algorithms , vol.18 , pp. 71-90
    • Bristeau, M.-O.1    Erhel, J.2
  • 4
    • 0003541860 scopus 로고
    • A survey of preconditioned iterative methods
    • Longman Scientific and Technical, Harlow, UK
    • A. BRUASET, A Survey of Preconditioned Iterative Methods, Pitman Res. Notes Math. Ser. 328, Longman Scientific and Technical, Harlow, UK, 1995.
    • (1995) Pitman Res. Notes Math. Ser. , vol.328
    • Bruaset, A.1
  • 6
    • 0031261346 scopus 로고    scopus 로고
    • Analysis of projection methods for solving linear systems with multiple right-hand sides
    • T. F. CHAN AND W. L. WAN, Analysis of projection methods for solving linear systems with multiple right-hand sides, SIAM J. Sci. Comput., 18 (1997), pp. 1698-1721.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 1698-1721
    • Chan, T.F.1    Wan, W.L.2
  • 7
    • 0031488469 scopus 로고    scopus 로고
    • Deflated and augmented Krylov subspace techniques
    • A. CHAPMAN AND Y. SAAD, Deflated and augmented Krylov subspace techniques, Numer. Linear Algebra Appl., 4 (1997), pp. 43-66.
    • (1997) Numer. Linear Algebra Appl. , vol.4 , pp. 43-66
    • Chapman, A.1    Saad, Y.2
  • 9
    • 0032367198 scopus 로고    scopus 로고
    • On the performance of various adaptive preconditioned GMRES strategies
    • J. ERHEL AND K. BURRAGE, On the performance of various adaptive preconditioned GMRES strategies, Numer. Linear Algebra Appl., 5 (1998), pp. 101-121.
    • (1998) Numer. Linear Algebra Appl. , vol.5 , pp. 101-121
    • Erhel, J.1    Burrage, K.2
  • 10
    • 0030143587 scopus 로고    scopus 로고
    • Restarted GMRES preconditioned by deflation
    • J. ERHEL, K. BURRAGE, AND B. POHL, Restarted GMRES preconditioned by deflation, J. Comput. Appl. Math., 69 (1996), pp. 303-318.
    • (1996) J. Comput. Appl. Math. , vol.69 , pp. 303-318
    • Erhel, J.1    Burrage, K.2    Pohl, B.3
  • 11
    • 0028465936 scopus 로고
    • Extending substructure based iterative solvers to multiple load and repeated analyses
    • C. FARHAT, L. CRIVELLI, AND F.-X. ROUX, Extending substructure based iterative solvers to multiple load and repeated analyses, Comput. Methods Appl. Mech. Engrg., 117 (1994), pp. 195-209.
    • (1994) Comput. Methods Appl. Mech. Engrg. , vol.117 , pp. 195-209
    • Farhat, C.1    Crivelli, L.2    Roux, F.-X.3
  • 12
    • 0004116606 scopus 로고
    • Projection techniques for iterative solution of Ax = b with successive right-hand sides
    • NASA Langley Research Center, Hampton, VA
    • P. F. FISHER, Projection Techniques for Iterative Solution of Ax = b with Successive Right-Hand Sides, ICASE Tech. Report 93-90, NASA Langley Research Center, Hampton, VA, 1993.
    • (1993) ICASE Tech. Report , pp. 93-190
    • Fisher, P.F.1
  • 17
    • 0342602167 scopus 로고
    • A restarted GMRES method augmented with eigenvectors
    • R. B. MORGAN, A restarted GMRES method augmented with eigenvectors, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 1154-1171.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 1154-1171
    • Morgan, R.B.1
  • 18
    • 85037779558 scopus 로고    scopus 로고
    • Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations
    • to appear
    • R. B. MORGAN, Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations, SIAM J. Matrix Anal. Appl., to appear.
    • SIAM J. Matrix Anal. Appl.
    • Morgan, R.B.1
  • 19
    • 0023331865 scopus 로고
    • Deflation of conjugate gradients with applications to boundary value problems
    • R. A. NICOLAIDES, Deflation of conjugate gradients with applications to boundary value problems, SIAM J. Numer. Anal., 24 (1987), pp. 355-365.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 355-365
    • Nicolaides, R.A.1
  • 20
    • 0001084178 scopus 로고
    • The block conjugate gradient algorithm and related methods
    • D. P. O'LEARY, The block conjugate gradient algorithm and related methods, Linear Algebra Appl., 29 (1980), pp. 293-322.
    • (1980) Linear Algebra Appl. , vol.29 , pp. 293-322
    • O'Leary, D.P.1
  • 21
    • 0025226277 scopus 로고
    • A new implementation of the Lanczos method in linear problems
    • M. PAPADRAKAKIS AND S. SMEROU, A new implementation of the Lanczos method in linear problems, Internat. J. Numer. Methods in Engrg., 29 (1990), pp. 141-159.
    • (1990) Internat. J. Numer. Methods in Engrg. , vol.29 , pp. 141-159
    • Papadrakakis, M.1    Smerou, S.2
  • 22
    • 0001008883 scopus 로고
    • A new look at the Lanczos algorithm for solving symmetric systems of linear equations
    • B. PARLETT, A new look at the Lanczos algorithm for solving symmetric systems of linear equations, Linear Algebra Appl., 29 (1980), pp. 323-346.
    • (1980) Linear Algebra Appl. , vol.29 , pp. 323-346
    • Parlett, B.1
  • 24
    • 84966225678 scopus 로고
    • On the lanczos method for solving symmetric linear systems with several right-hand sides
    • Y. SAAD, On the Lanczos method for solving symmetric linear systems with several right-hand sides, Math. Comp., 178 (1987), pp. 651-662.
    • (1987) Math. Comp. , vol.178 , pp. 651-662
    • Saad, Y.1
  • 27
    • 21444444506 scopus 로고    scopus 로고
    • Further results on the convergence behavior of conjugate-gradients and Ritz values
    • G. SLEIJPEN AND A. VAN DER SLUIS, Further results on the convergence behavior of conjugate-gradients and Ritz values, Linear Algebra Appl., 246 (1996), pp. 233-278.
    • (1996) Linear Algebra Appl. , vol.246 , pp. 233-278
    • Sleijpen, G.1    Van Der Sluis, A.2
  • 28
    • 0024767311 scopus 로고
    • A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields
    • C. SMITH, A. PETERSON, AND R. MITTRA, A conjugate gradient algorithm for the treatment of multiple incident electromagnetic fields, IEEE Trans. Antennas and Propagation, 37 (1989), pp. 1490-1493.
    • (1989) IEEE Trans. Antennas and Propagation , vol.37 , pp. 1490-1493
    • Smith, C.1    Peterson, A.2    Mittra, R.3
  • 29
    • 0001403122 scopus 로고
    • The rate of convergence of conjugate gradients
    • A. VAN DER SLUIS AND H. VAN DER VORST, The rate of convergence of conjugate gradients, Numer. Math., 48 (1986), pp. 543-560.
    • (1986) Numer. Math. , vol.48 , pp. 543-560
    • Van Der Sluis, A.1    Van Der Vorst, H.2
  • 30
    • 0001646445 scopus 로고
    • An iterative method for solving f(A)x = b using Krylov subspace information obtained for the symmetric positive definite matrix A
    • H. VAN DER VORST, An iterative method for solving f(A)x = b using Krylov subspace information obtained for the symmetric positive definite matrix A, J. Comput. Appl. Math., 18 (1987), pp. 249-263.
    • (1987) J. Comput. Appl. Math. , vol.18 , pp. 249-263
    • Van Der Vorst, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.