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Volumn 28, Issue 4, 2006, Pages 1069-1082

Inexact inverse iteration with variable shift for nonsymmetric generalized eigenvalue problems

Author keywords

Eigenvalue approximation; Inverse iteration; Iterative methods

Indexed keywords

APPROXIMATION ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; PROBLEM SOLVING;

EID: 35348979635     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/050623255     Document Type: Conference Paper
Times cited : (23)

References (25)
  • 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
  • 5
    • 0033293064 scopus 로고    scopus 로고
    • Inexact preconditioned conjugate gradient method with inner-outer iteration
    • G. H. GOLUB AND Q. YE, Inexact preconditioned conjugate gradient method with inner-outer iteration, SIAM J. Sci. Comput., 21 (1999), pp. 1305-1320.
    • (1999) SIAM J. Sci. Comput , vol.21 , pp. 1305-1320
    • GOLUB, G.H.1    YE, Q.2
  • 6
    • 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
  • 7
    • 0042496332 scopus 로고    scopus 로고
    • A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems
    • Z. JIA, A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems, Linear Algebra Appl., 270 (1998), pp. 171-189.
    • (1998) Linear Algebra Appl , vol.270 , pp. 171-189
    • JIA, Z.1
  • 8
    • 0033098309 scopus 로고    scopus 로고
    • An improved subspace iteration method with shifting
    • H.-J. JUNG, M.-C. KIM, AND I.-W. LEE, An improved subspace iteration method with shifting, Comput. & Structures, 70 (1999), pp. 625-633.
    • (1999) Comput. & Structures , vol.70 , pp. 625-633
    • JUNG, H.-J.1    KIM, M.-C.2    LEE, I.-W.3
  • 9
    • 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
  • 10
    • 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
  • 12
    • 0036058969 scopus 로고    scopus 로고
    • Implicitly restarted Arnoldi methods and subspace iteration
    • R. B. LEHOUCQ, Implicitly restarted Arnoldi methods and subspace iteration, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 551-562.
    • (2001) SIAM J. Matrix Anal. Appl , vol.23 , pp. 551-562
    • LEHOUCQ, R.B.1
  • 13
    • 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. Statist. Comput., 7 (1986), pp. 817-825.
    • (1986) SIAM J. Sci. Statist. Comput , vol.7 , pp. 817-825
    • MORGAN, R.B.1    SCOTT, D.S.2
  • 14
    • 0035586115 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration!; Extrema of the Rayleigh quotient
    • K. NEYMEYR, A geometric theory for preconditioned inverse iteration!; 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
    • 0035585865 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration II: Convergence estimates
    • K. NEYMEYR, A geometric theory for preconditioned inverse iteration II: Convergence estimates, Linear Algebra Appl., 322 (2001), pp. 87-104.
    • (2001) Linear Algebra Appl , vol.322 , pp. 87-104
    • NEYMEYR, K.1
  • 16
    • 84966257139 scopus 로고
    • The Rayleigh quotient iteration and some generalizations for nonnormal matrices
    • B. N. PARLETT, The Rayleigh quotient iteration and some generalizations for nonnormal matrices, Math. Comp., 28 (1974), pp. 679-693.
    • (1974) Math. Comp , vol.28 , pp. 679-693
    • PARLETT, B.N.1
  • 18
    • 0000080063 scopus 로고
    • Inverse iteration, ill-conditioned equations and Newton's method
    • G. PETERS AND J. H. 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.H.2
  • 19
    • 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
  • 20
    • 0001622217 scopus 로고
    • Solving sparse symmetric generalized eigenvalue problems without factorization
    • D. S. SCOTT, Solving sparse symmetric generalized eigenvalue problems without factorization, SIAM J, Numer. Anal., 18 (1981), pp. 102-110.
    • (1981) SIAM J, Numer. Anal , vol.18 , pp. 102-110
    • SCOTT, D.S.1
  • 21
    • 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
  • 22
    • 0030560293 scopus 로고    scopus 로고
    • A Jacobi-Davidson iteration method for linear eigenvalue problems
    • G. L. G. SLEUPEN 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
    • SLEUPEN, G.L.G.1    VAN DER VORST, H.A.2
  • 23
    • 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
  • 24
    • 0033131191 scopus 로고    scopus 로고
    • An accelerated subspace iteration method for generalized eigenproblems
    • X. WANG AND J. ZHOU, An accelerated subspace iteration method for generalized eigenproblems, Comput. & Structures, 71 (1999), pp. 293-301.
    • (1999) Comput. & Structures , vol.71 , pp. 293-301
    • WANG, X.1    ZHOU, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.