메뉴 건너뛰기




Volumn 416, Issue 2-3, 2006, Pages 389-413

Inexact inverse iteration for symmetric matrices

Author keywords

Inverse iteration; Iterative methods; Preconditioned MINRES; Rayleigh quotient iteration

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; INVERSE PROBLEMS; ITERATIVE METHODS; LINEAR SYSTEMS; PROBLEM SOLVING;

EID: 33646946291     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2005.11.019     Document Type: Article
Times cited : (43)

References (22)
  • 1
    • 33646913749 scopus 로고    scopus 로고
    • Jörg Berns-Müller, Inexact inverse iteration using Galerkin Krylov solvers, Ph.D. Thesis, University of Bath, 2003.
  • 2
    • 0000441576 scopus 로고
    • Convergence of infinite products of matrices and inner-outer iteration schemes
    • Bru R., Elsner E., and Neumann M. Convergence of infinite products of matrices and inner-outer iteration schemes. ETNA 2 (1994) 183-193
    • (1994) ETNA , vol.2 , pp. 183-193
    • Bru, R.1    Elsner, E.2    Neumann, M.3
  • 3
    • 0030079943 scopus 로고    scopus 로고
    • Nested Krylov methods based on GCR
    • de Sturler E. Nested Krylov methods based on GCR. J. Comput. Appl. Math. 67 (1997) 15-41
    • (1997) J. Comput. Appl. Math. , vol.67 , pp. 15-41
    • de Sturler, E.1
  • 4
    • 0002274317 scopus 로고
    • Improving the accuracy of computed eigenvalues and eigenvectors
    • Dongarra J.J., Moler C.B., and Wilkinson J.H. Improving the accuracy of computed eigenvalues and eigenvectors. SIAM J. Numer. Anal. 20 1 (1983) 23-45
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.1 , pp. 23-45
    • Dongarra, J.J.1    Moler, C.B.2    Wilkinson, J.H.3
  • 5
    • 0033293064 scopus 로고    scopus 로고
    • Inexact preconditioned conjugate gradient method with inner-outer iteration
    • Golub G.H., and Ye Q. Inexact preconditioned conjugate gradient method with inner-outer iteration. SIAM J. Sci. Comput. 21 4 (1999) 1305-1320
    • (1999) SIAM J. Sci. Comput. , vol.21 , Issue.4 , pp. 1305-1320
    • Golub, G.H.1    Ye, Q.2
  • 6
    • 0041730764 scopus 로고    scopus 로고
    • Inexact inverse iteration for generalized eigenvalue problems
    • Golub G.H., and Ye Q. Inexact inverse iteration for generalized eigenvalue problems. BIT 40 4 (2000) 671-684
    • (2000) BIT , vol.40 , Issue.4 , pp. 671-684
    • Golub, G.H.1    Ye, Q.2
  • 8
    • 0001264814 scopus 로고    scopus 로고
    • Numerical behavior of the modified Gram-Schmidt GMRES implementation
    • Greenbaum A., Rozložník M., and Strakoš Z. Numerical behavior of the modified Gram-Schmidt GMRES implementation. BIT 37 3 (1997) 706-719
    • (1997) BIT , vol.37 , Issue.3 , pp. 706-719
    • Greenbaum, A.1    Rozložník, M.2    Strakoš, Z.3
  • 10
    • 0000522446 scopus 로고    scopus 로고
    • Preconditioned eigensolvers-an oxymoron?
    • Knyazev A.V. Preconditioned eigensolvers-an oxymoron?. Electron. Trans. Numer. Anal. 7 (1998) 104-123
    • (1998) Electron. Trans. Numer. Anal. , vol.7 , pp. 104-123
    • Knyazev, A.V.1
  • 11
    • 0036223489 scopus 로고    scopus 로고
    • Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method
    • Knyazev A.V. Toward the optimal preconditioned eigensolver: locally optimal block preconditioned conjugate gradient method. SIAM J. Sci. Comput. 23 2 (2001) 517-541
    • (2001) SIAM J. Sci. Comput. , vol.23 , Issue.2 , pp. 517-541
    • Knyazev, A.V.1
  • 12
    • 32044463478 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration. iii: A short and sharp convergence estimate for generalized eigenvalue problems
    • Knyazev A.V., and Neymeyr K. A geometric theory for preconditioned inverse iteration. iii: A short and sharp convergence estimate for generalized eigenvalue problems. Linear Algebra Appl. 358 (2003) 95-114
    • (2003) Linear Algebra Appl. , vol.358 , pp. 95-114
    • Knyazev, A.V.1    Neymeyr, K.2
  • 13
    • 33646950914 scopus 로고    scopus 로고
    • An inexact inverse iteration for large sparse eigenvalue problems
    • Lai Y.-L., Lin K.-Y., and Wen-Wei L. An inexact inverse iteration for large sparse eigenvalue problems. Numer. Linear Algebra Appl. 1 (1997) 1-13
    • (1997) Numer. Linear Algebra Appl. , vol.1 , pp. 1-13
    • Lai, Y.-L.1    Lin, K.-Y.2    Wen-Wei, L.3
  • 14
    • 0042415256 scopus 로고    scopus 로고
    • Convergence analysis of inexact Rayleigh quotient iterations
    • Notay Y. Convergence analysis of inexact Rayleigh quotient iterations. SIAM J. Matrix Anal. Appl. 24 (2001) 627-644
    • (2001) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 627-644
    • Notay, Y.1
  • 15
    • 34250951234 scopus 로고
    • On the convergence of the Rayleigh quotient iteration for the computation of the characteristic roots and vectors. I
    • Ostrowski A.M. On the convergence of the Rayleigh quotient iteration for the computation of the characteristic roots and vectors. I. Arch. Rat. Mech. Anal. 1 (1957) 233-241
    • (1957) Arch. Rat. Mech. Anal. , vol.1 , pp. 233-241
    • Ostrowski, A.M.1
  • 16
    • 0016555955 scopus 로고
    • Solution of sparse indefinite systems of linear equations
    • Paige C.C., and Saunders M.A. Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12 (1975) 617-629
    • (1975) SIAM J. Numer. Anal. , vol.12 , pp. 617-629
    • Paige, C.C.1    Saunders, M.A.2
  • 18
    • 33646920261 scopus 로고    scopus 로고
    • Ulrich Rüde, W. Schmid, Inverse multigrid correction for generalized eigenvalue computations, Technical Report, Universität Augsburg, September 1995.
  • 19
    • 0041064557 scopus 로고
    • The method of conjugate gradients used in inverse iteration
    • Ruhe A., and Wiberg T. The method of conjugate gradients used in inverse iteration. BIT 12 (1972) 543-554
    • (1972) BIT , vol.12 , pp. 543-554
    • Ruhe, A.1    Wiberg, T.2
  • 20
    • 0009924727 scopus 로고    scopus 로고
    • Inexact Rayleigh quotient-type methods for eigenvalue computations
    • Simoncini V., and Eldén L. Inexact Rayleigh quotient-type methods for eigenvalue computations. BIT 42 1 (2002) 159-182
    • (2002) BIT , vol.42 , Issue.1 , pp. 159-182
    • Simoncini, V.1    Eldén, L.2
  • 21
    • 0001917562 scopus 로고    scopus 로고
    • Efficient expansion of subspaces in the Jacobi-Davidson method for standard and generalized eigenproblems
    • Sleijpen G.L.G., van der Vorst H.A., and Meijerink E. Efficient expansion of subspaces in the Jacobi-Davidson method for standard and generalized eigenproblems. ETNA 7 (1998) 75-89
    • (1998) ETNA , vol.7 , pp. 75-89
    • Sleijpen, G.L.G.1    van der Vorst, H.A.2    Meijerink, E.3
  • 22
    • 0033479131 scopus 로고    scopus 로고
    • The effects of inexact solvers in algorithms for symmetric eigenvalue problems
    • Smit P., and Paardekooper M.H.C. The effects of inexact solvers in algorithms for symmetric eigenvalue problems. Linear Algebra Appl. 287 (1999) 337-357
    • (1999) Linear Algebra Appl. , vol.287 , pp. 337-357
    • Smit, P.1    Paardekooper, M.H.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.