메뉴 건너뛰기




Volumn 47, Issue 1, 2007, Pages 27-44

Convergence of inexact inverse iteration with application to preconditioned iterative solves

Author keywords

Inverse iteration; Newton's method; Preconditioned iterative methods

Indexed keywords


EID: 33947213805     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-006-0100-1     Document Type: Article
Times cited : (35)

References (22)
  • 1
    • 21444446076 scopus 로고    scopus 로고
    • A general view of minimally extended systems for simple bifurcation points
    • E. L. Allgower and H. Schwetlick, A general view of minimally extended systems for simple bifurcation points, ZAMM Z. Angew. Math. Mech., 77 (1997), pp. 83-98.
    • (1997) ZAMM Z. Angew. Math. Mech , vol.77 , pp. 83-98
    • Allgower, E.L.1    Schwetlick, H.2
  • 2
    • 33646946291 scopus 로고    scopus 로고
    • Inexact inverse iteration for symmetric matrices
    • J. Berns-Müller, I. G. Graham, and A. Spence, Inexact inverse iteration for symmetric matrices, Linear Algebra Appl., 416 (2006), pp. 389-413.
    • (2006) Linear Algebra Appl , vol.416 , pp. 389-413
    • Berns-Müller, J.1    Graham, I.G.2    Spence, A.3
  • 4
    • 35348979635 scopus 로고    scopus 로고
    • J. Berna-Müller and A. Spence, Inexact inverse iteration and the nonsymmetric generalized eigenvalue problem, 2006. To appear in SIAM J. Matrix Anal. Appl.
    • J. Berna-Müller and A. Spence, Inexact inverse iteration and the nonsymmetric generalized eigenvalue problem, 2006. To appear in SIAM J. Matrix Anal. Appl.
  • 6
    • 33947266772 scopus 로고    scopus 로고
    • J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics in Applied Mathematics, 16, SIAM, Philadelphia, PA, 1996. Unabridged, corrected reprint of the 1983 original.
    • J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics in Applied Mathematics, vol. 16, SIAM, Philadelphia, PA, 1996. Unabridged, corrected reprint of the 1983 original.
  • 7
    • 33747151020 scopus 로고    scopus 로고
    • Newton Methods for Nonlinear Problems
    • Springer, Berlin, Heidelberg
    • P. Deuflhard, Newton Methods for Nonlinear Problems, Springer Series in Computational Mathematics, vol. 35, Springer, Berlin, Heidelberg, 2004.
    • (2004) Springer Series in Computational Mathematics , vol.35
    • Deuflhard, P.1
  • 8
    • 0032216898 scopus 로고    scopus 로고
    • The geometry of algorithms with orthogonality constraints
    • A. Edelman, T. Arias, and S. T. Smith, The geometry of algorithms with orthogonality constraints, SIAM J. Matrix Anal. Appl., 20 (1999), pp. 303-353.
    • (1999) SIAM J. Matrix Anal. Appl , vol.20 , pp. 303-353
    • Edelman, A.1    Arias, T.2    Smith, S.T.3
  • 9
    • 0041730764 scopus 로고    scopus 로고
    • Inexact inverse iteration for generalized eigenvalue problems
    • G. H. Golub and Q. Ye, Inexact inverse iteration for generalized eigenvalue problems, BIT, 40 (2000), pp. 671-684.
    • (2000) BIT , vol.40 , pp. 671-684
    • Golub, G.H.1    Ye, Q.2
  • 10
    • 0000276399 scopus 로고
    • Numerical solution of bifurcation and nonlinear eigenvalue problems
    • Theory, P. H. Rabinowitz, ed, Academic Press, New York
    • H. B. Keller, Numerical solution of bifurcation and nonlinear eigenvalue problems, in Applications of Bifurcation Theory, P. H. Rabinowitz, ed., Academic Press, New York, 1977, pp. 359-384.
    • (1977) Applications of Bifurcation , pp. 359-384
    • Keller, H.B.1
  • 12
    • 0036223489 scopus 로고    scopus 로고
    • Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method
    • A. V. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM J. Sci. Comput., 23 (2001), pp. 517-541.
    • (2001) SIAM J. Sci. Comput , vol.23 , pp. 517-541
    • Knyazev, A.V.1
  • 13
    • 33646950914 scopus 로고    scopus 로고
    • An inexact inverse iteration for large sparse eigenvalue problems
    • Y.-L. Lai, K.-Y. Lin, and L. Wen-Wei, An inexact inverse iteration for large sparse eigenvalue problems, Numer. Linear Algebra Appl., 1 (1997), pp. 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
    • 0035586115 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration I: Extrema of the Rayleigh quotient
    • K. Neymeyr, A geometric theory for preconditioned inverse iteration I: Extrema of the Rayleigh quotient, Linear Algebra Appl., 322 (2001), pp. 61-85.
    • (2001) Linear Algebra Appl , vol.322 , pp. 61-85
    • Neymeyr, K.1
  • 15
    • 0000080063 scopus 로고
    • Inverse iteration, ill-conditioned equations and Newton's method
    • G. Peters and J. Wilkinson, Inverse iteration, ill-conditioned equations and Newton's method, SIAM Rev., 21 (1979), pp. 339-360.
    • (1979) SIAM Rev , vol.21 , pp. 339-360
    • Peters, G.1    Wilkinson, J.2
  • 16
    • 0041064557 scopus 로고
    • The method of conjugate gradients used in inverse iteration
    • A. Ruhe and T. Wiberg, The method of conjugate gradients used in inverse iteration, BIT, 12 (1972), pp. 543-554.
    • (1972) BIT , vol.12 , pp. 543-554
    • Ruhe, A.1    Wiberg, T.2
  • 18
    • 22844455049 scopus 로고    scopus 로고
    • A generalized Rayleigh quotient iteration for computing simple eigenvalues of nonnormal matrices
    • H. Schwetlick and R. Lösche, A generalized Rayleigh quotient iteration for computing simple eigenvalues of nonnormal matrices, ZAMM Z. Angew. Math. Mech., 80 (2000), pp. 9-25.
    • (2000) ZAMM Z. Angew. Math. Mech , vol.80 , pp. 9-25
    • Schwetlick, H.1    Lösche, R.2
  • 19
    • 0009924727 scopus 로고    scopus 로고
    • Inexact Rayleigh quotient-type methods for eigenvalue computations
    • V. Simoncini and L. Eldén, Inexact Rayleigh quotient-type methods for eigenvalue computations, BIT, 42 (2002), pp. 159-182.
    • (2002) BIT , vol.42 , pp. 159-182
    • Simoncini, V.1    Eldén, L.2
  • 20
    • 0033479131 scopus 로고    scopus 로고
    • The effects of inexact solvers in algorithms for symmetric eigenvalue problems
    • P. Smit and M. H. C. Paardekooper, The effects of inexact solvers in algorithms for symmetric eigenvalue problems, Linear Algebra Appl., 287 (1999), pp. 337-357.
    • (1999) Linear Algebra Appl , vol.287 , pp. 337-357
    • Smit, P.1    Paardekooper, M.H.C.2
  • 21
    • 0001139414 scopus 로고
    • Realistic error bounds for a simple eigenvalue and its associated eigenvector
    • H. Symm and J. Wilkinson, Realistic error bounds for a simple eigenvalue and its associated eigenvector, Numer. Math., 35 (1980), pp. 113-126.
    • (1980) Numer. Math , vol.35 , pp. 113-126
    • Symm, H.1    Wilkinson, J.2
  • 22
    • 0043023228 scopus 로고
    • Nichtlineare Behandlung von Eigenwertaufgaben
    • H. Unger, Nichtlineare Behandlung von Eigenwertaufgaben, ZAMM Z. Angew. Math. Mech., 30 (1950), pp. 281-282.
    • (1950) ZAMM Z. Angew. Math. Mech , vol.30 , pp. 281-282
    • Unger, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.