메뉴 건너뛰기




Volumn 311, Issue 1-3, 2000, Pages 45-60

Relative perturbation theory: IV. sin 2θ theorems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034418507     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(00)00077-X     Document Type: Article
Times cited : (7)

References (31)
  • 1
    • 0025445384 scopus 로고
    • Computing accurate eigensystems of scaled diagonally dominant matrices
    • Barlow J., Demmel J. Computing accurate eigensystems of scaled diagonally dominant matrices. SIAM J. Numer. Anal. 27:1990;762-791.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 762-791
    • Barlow, J.1    Demmel, J.2
  • 2
    • 0033632911 scopus 로고    scopus 로고
    • The p-relative distance is a metric
    • to appear
    • A. Barrlund, The p -relative distance is a metric, SIAM J. Matrix Anal. Appl. (1998), to appear.
    • (1998) SIAM J. Matrix Anal. Appl.
    • Barrlund, A.1
  • 3
    • 0014751986 scopus 로고
    • The rotation of eigenvectors by a perturbation. III
    • Davis C., Kahan W. The rotation of eigenvectors by a perturbation. III. SIAM J. Numer. Anal. 7:1970;1-46.
    • (1970) SIAM J. Numer. Anal. , vol.7 , pp. 1-46
    • Davis, C.1    Kahan, W.2
  • 4
    • 0026238244 scopus 로고
    • The bidiagonal singular value decomposition and Hamiltonian mechanics
    • Deift P., Demmel J., Li L.-C., Tomei C. The bidiagonal singular value decomposition and Hamiltonian mechanics. SIAM J. Numer. Anal. 28:1991;1463-1516.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1463-1516
    • Deift, P.1    Demmel, J.2    Li, L.-C.3    Tomei, C.4
  • 6
    • 0033633262 scopus 로고    scopus 로고
    • Accurate SVDs of structure matrices
    • J. Demmel, Accurate SVDs of structure matrices, SIAM J. Matrix Anal. Appl. 21 (2000) 562-580.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 562-580
    • Demmel, J.1
  • 7
    • 38249003695 scopus 로고
    • On computing accurate singular values and eigenvalues of matrices with acyclic graphs
    • Demmel J., Gragg W. On computing accurate singular values and eigenvalues of matrices with acyclic graphs. Linear Algebra Appl. 185:1993;203-217.
    • (1993) Linear Algebra Appl. , vol.185 , pp. 203-217
    • Demmel, J.1    Gragg, W.2
  • 8
    • 0001192187 scopus 로고
    • Accurate singular values of bidiagonal matrices
    • Demmel J., Kahan W. Accurate singular values of bidiagonal matrices. SIAM J. Sci. Statist. Comput. 11:1990;873-912.
    • (1990) SIAM J. Sci. Statist. Comput. , vol.11 , pp. 873-912
    • Demmel, J.1    Kahan, W.2
  • 9
    • 21144468781 scopus 로고
    • Jacobi's method is more accurate than QR
    • J. Demmel, K. Veselić, Jacobi's method is more accurate than QR, SIAM J. Matrix Anal. Appl. 13 (1992) 1204-1245.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 1204-1245
    • Demmel, J.1    Veselić, K.2
  • 11
    • 0008486996 scopus 로고
    • Results on the relative perturbation of the singular values of a matrix
    • DiLena G., Peluso R.I., Piazza G. Results on the relative perturbation of the singular values of a matrix. BIT. 33:1993;647-653.
    • (1993) BIT , vol.33 , pp. 647-653
    • Dilena, G.1    Peluso, R.I.2    Piazza, G.3
  • 12
    • 0009285515 scopus 로고
    • Relative perturbation bounds for eigenspaces and singular vector subspaces
    • in: J.G. Lewis (Ed.), SIAM, Philadelphia, PA
    • S.C. Eisenstat, I.C.F. Ipsen, Relative perturbation bounds for eigenspaces and singular vector subspaces, in: J.G. Lewis (Ed.), Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, SIAM, Philadelphia, PA, 1994, pp. 62-66.
    • (1994) Proceedings of the Fifth SIAM Conference on Applied Linear Algebra , pp. 62-66
    • Eisenstat, S.C.1    Ipsen, I.C.F.2
  • 13
    • 0001371240 scopus 로고
    • Relative perturbation techniques for singular value problems
    • Eisenstat S.C., Ipsen I.C.F. Relative perturbation techniques for singular value problems. SIAMJ. Numer. Anal. 32:1995;1972-1988.
    • (1995) SIAMJ. Numer. Anal. , vol.32 , pp. 1972-1988
    • Eisenstat, S.C.1    Ipsen, I.C.F.2
  • 14
    • 21344496407 scopus 로고
    • Accurate singular values and differential qd algorithms
    • Fernando K.V., Parlett B.N. Accurate singular values and differential qd algorithms. Numer. Math. 67:1994;191-229.
    • (1994) Numer. Math. , vol.67 , pp. 191-229
    • Fernando, K.V.1    Parlett, B.N.2
  • 16
    • 85011525782 scopus 로고    scopus 로고
    • Relative perturbation results for matrix eigenvalues and singular values
    • I.C.F. Ipsen, Relative perturbation results for matrix eigenvalues and singular values, Acta Numerica 7 (1998) 151-201.
    • (1998) Acta Numerica , vol.7 , pp. 151-201
    • Ipsen, I.C.F.1
  • 17
    • 0004222768 scopus 로고
    • Technical Report CS41, Computer Science Department, Stanford University, Stanford, CA, (revised June 1968)
    • W. Kahan, Accurate eigenvalues of a symmetric tridiagonal matrix, Technical Report CS41, Computer Science Department, Stanford University, Stanford, CA, 1966 (revised June 1968).
    • (1966) Accurate Eigenvalues of a Symmetric Tridiagonal Matrix
    • Kahan, W.1
  • 18
    • 0033479425 scopus 로고    scopus 로고
    • The Lidskii-Mirsky-Wielandt theorem - Additive and multiplicative versions
    • Li C.-K., Mathias R. The Lidskii-Mirsky-Wielandt theorem - additive and multiplicative versions. Numer. Math. 81:1999;377-413.
    • (1999) Numer. Math. , vol.81 , pp. 377-413
    • Li, C.-K.1    Mathias, R.2
  • 19
    • 84968490745 scopus 로고
    • On perturbations of matrix pencils with real spectra
    • Li R.-C. On perturbations of matrix pencils with real spectra. Math. Comput. 62:1994;231-265.
    • (1994) Math. Comput. , vol.62 , pp. 231-265
    • Li, R.-C.1
  • 20
    • 0032344743 scopus 로고    scopus 로고
    • Relative perturbation theory: I. Eigenvalue and singular value variations
    • Li R.-C. Relative perturbation theory: I. Eigenvalue and singular value variations. SIAM J. Matrix Anal. Appl. 19:1998;956-982.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.19 , pp. 956-982
    • Li, R.-C.1
  • 21
    • 0032216896 scopus 로고    scopus 로고
    • Relative perturbation theory: II. Eigenspace and singular subspace variations
    • Li R.-C. Relative perturbation theory: II. Eigenspace and singular subspace variations. SIAMJ. Matrix Anal. Appl. 20:1999;471-492.
    • (1999) SIAMJ. Matrix Anal. Appl. , vol.20 , pp. 471-492
    • Li, R.-C.1
  • 22
    • 0039419182 scopus 로고    scopus 로고
    • Relative perturbation theory: (III) more bounds on eigenvalue variation
    • Li R.-C. Relative perturbation theory: (III) more bounds on eigenvalue variation. Linear Algebra Appl. 266:1997;337-345.
    • (1997) Linear Algebra Appl. , vol.266 , pp. 337-345
    • Li, R.-C.1
  • 23
    • 0033632301 scopus 로고    scopus 로고
    • A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory
    • Li R.-C. A bound on the solution to a structured Sylvester equation with an application to relative perturbation theory. SIAM J. Matrix Anal. Appl. 21:2000;440-445.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 440-445
    • Li, R.-C.1
  • 24
    • 0034391393 scopus 로고    scopus 로고
    • A new relative perturbation theorem for singular subspaces
    • to appear
    • R.-C. Li, G.W. Stewart, A new relative perturbation theorem for singular subspaces, Linear Algebra Appl. (2000), to appear.
    • (2000) Linear Algebra Appl.
    • Li, R.-C.1    Stewart, G.W.2
  • 25
    • 0042375241 scopus 로고
    • Accurate eigensystem computations by Jacobi methods
    • Mathias R. Accurate eigensystem computations by Jacobi methods. SIAM J. Matrix Anal. Appl. 16:1995;977-1003.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , pp. 977-1003
    • Mathias, R.1
  • 26
    • 0031493430 scopus 로고    scopus 로고
    • Spectral perturbation bounds for positive definite matrices
    • Mathias R. Spectral perturbation bounds for positive definite matrices. SIAM J. Matrix Anal. Appl. 18:1997;959-980.
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , pp. 959-980
    • Mathias, R.1
  • 28
    • 0003651309 scopus 로고
    • Accurate symmetric eigenreduction by a Jacobi method
    • Ph.D. Thesis, Facbereich Mathematik
    • I. Slapničar, Accurate symmetric eigenreduction by a Jacobi method, Ph.D. Thesis, Fernuniversität - Gesamthochschule - Hagen, Facbereich Mathematik, 1992.
    • (1992) Fernuniversität - Gesamthochschule - Hagen
    • Slapničar, I.1
  • 29
    • 0038892101 scopus 로고
    • Perturbation bounds for eigenspaces of a definite matrix pair
    • Sun J.-G. Perturbation bounds for eigenspaces of a definite matrix pair. Numer. Math. 41:1983;321-343.
    • (1983) Numer. Math. , vol.41 , pp. 321-343
    • Sun, J.-G.1
  • 30
    • 0016926423 scopus 로고
    • Generalizing the singular value decomposition
    • C.F. Van Loan, Generalizing the singular value decomposition, SIAM J. Numer. Anal. 13 (1976) 76-83.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 76-83
    • Van Loan, C.F.1
  • 31
    • 0002790288 scopus 로고
    • Perturbation bounds in connection with singular value decomposition
    • Wedin P.-Å. Perturbation bounds in connection with singular value decomposition. BIT. 12:1972;99-111.
    • (1972) BIT , vol.12 , pp. 99-111
    • Wedin, P.-Å.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.