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Volumn 22, Issue 2, 2001, Pages 602-616

Thick-restart Lanczos method for large symmetric eigenvalue problems

Author keywords

Lanczos eigenvalue method; Partial reorthogonalization; Thick restart

Indexed keywords


EID: 0006377434     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479898334605     Document Type: Article
Times cited : (288)

References (29)
  • 1
    • 0002807741 scopus 로고
    • The principle of minimized iteration in the solution of the matrix eigenvalue problem
    • W. E. ARNOLDI, The principle of minimized iteration in the solution of the matrix eigenvalue problem, Quart. Appl. Math., 9 (1951), pp. 17-29.
    • (1951) Quart. Appl. Math. , vol.9 , pp. 17-29
    • Arnoldi, W.E.1
  • 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
    • Deflated and Augmented Krylov Subspace Techniques
    • Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, MN
    • A. CHAPMAN AND Y. SAAD, Deflated and Augmented Krylov Subspace Techniques, Tech. Rep. UMSI 95/181, Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, MN, 1995.
    • (1995) Tech. Rep. UMSI 95/181
    • Chapman, A.1    Saad, Y.2
  • 4
    • 0041397249 scopus 로고
    • Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Theory
    • Birkhäuser Boston, Boston, MA
    • J. CULLUM AND R. A. WILLOUGHBY, Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Theory, Progress in Scientific Computing 3, Birkhäuser Boston, Boston, MA, 1985.
    • (1985) Progress in Scientific Computing 3
    • Cullum, J.1    Willoughby, R.A.2
  • 5
    • 84966217951 scopus 로고
    • Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization
    • J. W. DANIEL, W. B. GRAGG, L. KAUFMAN, AND G. W. STEWART, Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comp., 30 (1976), pp. 772-795.
    • (1976) Math. Comp. , vol.30 , pp. 772-795
    • Daniel, J.W.1    Gragg, W.B.2    Kaufman, L.3    Stewart, G.W.4
  • 6
    • 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
  • 7
    • 0024665254 scopus 로고
    • Super-matrix methods
    • E. R. DAVIDSON, Super-matrix methods, Comput. Phys. Comm., 53 (1989), pp. 49-60.
    • (1989) Comput. Phys. Comm. , vol.53 , pp. 49-60
    • Davidson, E.R.1
  • 10
    • 0032131701 scopus 로고    scopus 로고
    • Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils
    • D. R. FOKKEMA, G. L. G. SLEIJPEN, AND H. A. VAN DER VORST, Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils, SIAM J. Sci. Comput., 20 (1999), pp. 94-125.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 94-125
    • Fokkema, D.R.1    Sleijpen, G.L.G.2    Van Der Vorst, H.A.3
  • 13
    • 0030502142 scopus 로고    scopus 로고
    • Deflation techniques for an implicitly restarted Arnoldi iteration
    • R. B. LEHOUCQ AND D. SORENSEN, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 789-821.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 789-821
    • Lehoucq, R.B.1    Sorensen, D.2
  • 14
    • 0000965239 scopus 로고
    • Computing interior eigenvalues of large matrices
    • R. B. MORGAN, Computing interior eigenvalues of large matrices, Linear Algebra Appl., 156 (1991), pp. 289-309.
    • (1991) Linear Algebra Appl. , vol.156 , pp. 289-309
    • 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. Comp., 65 (1996), pp. 1213-1230.
    • (1996) Math. Comp. , vol.65 , pp. 1213-1230
    • Morgan, R.B.1
  • 16
    • 0003358142 scopus 로고    scopus 로고
    • The Symmetric Eigenvalue Problem
    • SIAM, Philadelphia, PA
    • B. N. PARLETT, The Symmetric Eigenvalue Problem, Classics Appl. Math. 20, SIAM, Philadelphia, PA, 1998.
    • (1998) Classics Appl. Math. , vol.20
    • Parlett, B.N.1
  • 17
    • 84968487118 scopus 로고
    • The Lanczos algorithm with selective orthogonalization
    • B. N. PARLETT AND D. SCOTT, The Lanczos algorithm with selective orthogonalization, Math. Comp., 33 (1979), pp. 217-238.
    • (1979) Math. Comp. , vol.33 , pp. 217-238
    • Parlett, B.N.1    Scott, D.2
  • 19
    • 11744294271 scopus 로고
    • Analysis of Augmented Krylov Subspace Techniques
    • Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, MN
    • Y. SAAD, Analysis of Augmented Krylov Subspace Techniques, Tech. Rep. UMSI 95/175, Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, MN, 1995.
    • (1995) Tech. Rep. UMSI 95/175
    • Saad, Y.1
  • 22
    • 84968519566 scopus 로고
    • The Lanczos algorithm with partial reorthogonalization
    • H. D. SIMON, The Lanczos algorithm with partial reorthogonalization, Math. Comp., 42 (1984), pp. 115-136.
    • (1984) Math. Comp. , vol.42 , pp. 115-136
    • Simon, H.D.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. S. 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.S.1
  • 25
    • 0346555718 scopus 로고    scopus 로고
    • Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods
    • A. STATHOPOULOS, Y. SAAD, AND K. WU, Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods, SIAM J. Sci. Comput., 19 (1998), pp. 227-245.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 227-245
    • Stathopoulos, A.1    Saad, Y.2    Wu, K.3
  • 26
    • 0028401077 scopus 로고
    • Large scale electronic structure calculations using the Lanczos method
    • L.-W. WANG AND A. ZUNGER, Large scale electronic structure calculations using the Lanczos method, Computational Materials Science, 2 (1994), pp. 326-340.
    • (1994) Computational Materials Science , vol.2 , pp. 326-340
    • Wang, L.-W.1    Zunger, A.2
  • 27
    • 0042121939 scopus 로고    scopus 로고
    • Ph.D. thesis, University of Minnesota, Minneapolis, MN, An updated version also appears as Tech. Rep. TR97-038 at the Computer Science Department, University of Minnesota, Minneapolis, MN
    • K. WU, Preconditioned Techniques for Large Eigenvalue Problems, Ph.D. thesis, University of Minnesota, Minneapolis, MN, 1997. An updated version also appears as Tech. Rep. TR97-038 at the Computer Science Department, University of Minnesota, Minneapolis, MN.
    • (1997) Preconditioned Techniques for Large Eigenvalue Problems
    • Wu, K.1
  • 28
    • 0041621068 scopus 로고    scopus 로고
    • Thick-Restart Lanczos Method for Symmetric Eigenvalue Problems
    • Lawrence Berkeley National Laboratory, Berkeley, CA
    • K. WU AND H. SIMON, Thick-Restart Lanczos Method for Symmetric Eigenvalue Problems, Tech. Rep. 41412, Lawrence Berkeley National Laboratory, Berkeley, CA, 1998.
    • (1998) Tech. Rep. 41412
    • Wu, K.1    Simon, H.2
  • 29
    • 0042623025 scopus 로고    scopus 로고
    • Dynamic Restarting Schemes for Eigenvalue Problems
    • Lawrence Berkeley National Laboratory, Berkeley, CA
    • K. WU AND H. D. SIMON, Dynamic Restarting Schemes for Eigenvalue Problems, Tech. Rep. LBNL-42982, Lawrence Berkeley National Laboratory, Berkeley, CA, 1999.
    • (1999) Tech. Rep. LBNL-42982
    • Wu, K.1    Simon, H.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.