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Volumn 19, Issue 1, 1998, Pages 227-245

Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods

Author keywords

Arnoldi method; Davidson method; Deflation; Eigenvalue; Implicit restarting; Lanczos method; Preconditioning

Indexed keywords


EID: 0346555718     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827596304162     Document Type: Article
Times cited : (105)

References (29)
  • 2
    • 0002654780 scopus 로고
    • An implicitly restarted Lanczos method for large symmetric eigenvalue problems
    • D. CALVETTI, L. REICHEL, AND D. SORENSEN, An implicitly restarted Lanczos method for large symmetric eigenvalue problems, Electron. Trans. Numer. Anal., 2 (1994), pp. 1-21.
    • (1994) Electron. Trans. Numer. Anal. , vol.2 , pp. 1-21
    • Calvetti, D.1    Reichel, L.2    Sorensen, D.3
  • 3
    • 0040334323 scopus 로고
    • Tech. report 95-181, Supercomputing Institute, University of Minnesota, Minneapolis, MN
    • A. CHAPMAN AND Y. SAAD, Deflated and Augmented Krylov Subspace Techniques, Tech. report 95-181, Supercomputing Institute, University of Minnesota, Minneapolis, MN, 1995.
    • (1995) Deflated and Augmented Krylov Subspace Techniques
    • Chapman, A.1    Saad, Y.2
  • 4
    • 3542991752 scopus 로고    scopus 로고
    • Approximate inverse preconditioners via sparse-sparse iteration
    • to appear
    • E. CHOW AND Y. SAAD, Approximate inverse preconditioners via sparse-sparse iteration, SIAM J. Sci. Comput., to appear.
    • SIAM J. Sci. Comput.
    • Chow, E.1    Saad, Y.2
  • 7
    • 0041397249 scopus 로고
    • Lanczos Algorithms for Large Symmetric Eigenvalue Computations
    • Birkhäuser Boston, Boston, MA
    • J. CULLUM AND R. A. WILLOUGHBY, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 2, Programs of Progr. Sci. Comput. 4, Birkhäuser Boston, Boston, MA, 1985.
    • (1985) Programs of Progr. Sci. Comput. 4 , vol.2
    • Cullum, J.1    Willoughby, R.A.2
  • 8
    • 5344230920 scopus 로고
    • The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
    • E. R. DAVIDSON, The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices, J. Comput. Phys., 17 (1975), pp. 87-94.
    • (1975) J. Comput. Phys. , vol.17 , pp. 87-94
    • Davidson, E.R.1
  • 10
    • 0342496823 scopus 로고    scopus 로고
    • Jacobi-Davidson Style QR and QZ Algorithms for the Partial Reduction of Matrix Pencils
    • Tech. report 941, Department of Mathematics, University of Utrecht, the Netherlands, to appear
    • D. R. FOKKEMA, G. L. G. SLEIJPEN, AND H. A. VAN DER VORST, Jacobi-Davidson Style QR and QZ Algorithms for the Partial Reduction of Matrix Pencils, Tech. report 941, Department of Mathematics, University of Utrecht, the Netherlands, 1996; SIAM J. Sci. Comput., to appear.
    • (1996) SIAM J. Sci. Comput.
    • Fokkema, D.R.1    Sleijpen, G.L.G.2    Van Der Vorst, H.A.3
  • 11
    • 0000408399 scopus 로고
    • Modification of the Liu-Davidson method for obtaining one or simultaneously several eigensolutions of a large real-symmetric matrix
    • N. KOSUGI, Modification of the Liu-Davidson method for obtaining one or simultaneously several eigensolutions of a large real-symmetric matrix, J. Comput. Phys., 55 (1984), pp. 426-436.
    • (1984) J. Comput. Phys. , vol.55 , pp. 426-436
    • Kosugi, N.1
  • 14
    • 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
  • 15
    • 0030353046 scopus 로고    scopus 로고
    • On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
    • R. B. MORGAN, On restarting the Arnoldi method for large nonsymmetric eigenvalue problems, Math. Comput., 65 (1996), pp. 1213-1230.
    • (1996) Math. Comput. , vol.65 , pp. 1213-1230
    • Morgan, R.B.1
  • 16
    • 0001398614 scopus 로고
    • Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices
    • R. B. MORGAN AND D. S. SCOTT, Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices, SIAM J. Sci. Comput., 7 (1986), pp. 817-825.
    • (1986) SIAM J. Sci. Comput. , vol.7 , pp. 817-825
    • Morgan, R.B.1    Scott, D.S.2
  • 17
    • 28144442178 scopus 로고
    • Improved algorithms for the lowest eigenvalues and associated eigenvectors of large matrices
    • C. W. MURRAY, S. C. RACINE, AND E. R. DAVIDSON, Improved algorithms for the lowest eigenvalues and associated eigenvectors of large matrices, J. Comput. Phys., 103 (1992), pp. 382-389.
    • (1992) J. Comput. Phys. , vol.103 , pp. 382-389
    • Murray, C.W.1    Racine, S.C.2    Davidson, E.R.3
  • 18
    • 84936777186 scopus 로고
    • Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems
    • Y. SAAD, Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems, Math. Comp., 42 (1984), pp. 567-588.
    • (1984) Math. Comp. , vol.42 , pp. 567-588
    • Saad, Y.1
  • 20
    • 11744294271 scopus 로고
    • Tech. report 95-176, Supercomputing Institute, University of Minnesota, Minneapolis, MN
    • Y. SAAD, Analysis of Augmented Krylov Subspace Methods, Tech. report 95-176, Supercomputing Institute, University of Minnesota, Minneapolis, MN, 1995.
    • (1995) Analysis of Augmented Krylov Subspace Methods
    • Saad, Y.1
  • 21
    • 21144469414 scopus 로고
    • Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems
    • M. SADKANE, Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems, Numer. Math., 64 (1993), pp. 195-211.
    • (1993) Numer. Math. , vol.64 , pp. 195-211
    • Sadkane, M.1
  • 22
    • 0012665628 scopus 로고
    • The advantages of inverted operators in Rayleigh-Ritz approximations
    • D. S. SCOTT, The advantages of inverted operators in Rayleigh-Ritz approximations, SIAM J. Sci. and Statist. Comput., 3 (1982), pp. 68-75.
    • (1982) SIAM J. Sci. and Statist. Comput. , vol.3 , pp. 68-75
    • Scott, D.S.1
  • 23
    • 0030560293 scopus 로고    scopus 로고
    • A Jacobi-Davidson iteration method for linear eigenvalue problems
    • G. L. G. SLEIJPEN AND H. A. VAN DER VORST, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 401-425.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 401-425
    • Sleijpen, G.L.G.1    Van Der Vorst, H.A.2
  • 24
    • 0000322706 scopus 로고
    • Implicit application of polynomial filters in a K-step Arnoldi method
    • D. C. SORENSEN, Implicit application of polynomial filters in a K-step Arnoldi method, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 357-385.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 357-385
    • Sorensen, D.C.1
  • 25
    • 0028413862 scopus 로고
    • A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix
    • A. STATHOPOULOS AND C. FISCHER, A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix, Comput. Phys. Comm., 79 (1994), pp. 268-290.
    • (1994) Comput. Phys. Comm. , vol.79 , pp. 268-290
    • Stathopoulos, A.1    Fischer, C.2
  • 26
    • 0001390950 scopus 로고
    • Robust preconditioning of large, sparse, symmetric eigenvalue problems
    • A. STATHOPOULOS, Y. SAAD, AND C. FISCHER, Robust preconditioning of large, sparse, symmetric eigenvalue problems, J. Comput. Appl. Math., 64 (1995), pp. 197-215.
    • (1995) J. Comput. Appl. Math. , vol.64 , pp. 197-215
    • Stathopoulos, A.1    Saad, Y.2    Fischer, C.3
  • 27
    • 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), pp. 543-560.
    • (1986) Numer. Math. , vol.48 , pp. 543-560
    • Van Der Sluis, A.1    Van Der Vorst, H.A.2
  • 28
    • 0027701865 scopus 로고
    • The superlinear convergence behavior of GMRES
    • H. A. VAN DER VORST AND C. VUIK, The superlinear convergence behavior of GMRES, J. Comput. Appl. Math., 48 (1993), pp. 327-341.
    • (1993) J. Comput. Appl. Math. , vol.48 , pp. 327-341
    • Van Der Vorst, H.A.1    Vuik, C.2
  • 29
    • 84986435856 scopus 로고
    • A space-saving modification of Davidson's eigenvector algorithm
    • J. VAN LENTHE AND P. PULAY, A space-saving modification of Davidson's eigenvector algorithm, J. Comput. Chem., 11 (1990), pp. 1164-1168.
    • (1990) J. Comput. Chem. , vol.11 , pp. 1164-1168
    • Van Lenthe, J.1    Pulay, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.