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Volumn 17, Issue 3, 1996, Pages 570-593

Computational techniques for real logarithms of matrices

Author keywords

Conditioning; Eigendecomposition approaches; Error analysis; Implementations; Pad approximants; Real logarithm of a matrix; Series expansions

Indexed keywords


EID: 0030519907     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479894273614     Document Type: Article
Times cited : (68)

References (27)
  • 2
    • 0011545064 scopus 로고
    • Padé approximants, parts I and II
    • Addison-Wesley, Reading, MA
    • G. A. BAKER AND P. GRAVES-MORRIS, Padé Approximants, Parts I and II, Encyclopedia of Mathematics, vols. 13-14, Addison-Wesley, Reading, MA, 1981.
    • (1981) Encyclopedia of Mathematics , vol.13-14
    • Baker, G.A.1    Graves-Morris, P.2
  • 3
    • 0000954153 scopus 로고
    • A Schur method for the square root of a matrix
    • A. BJORCK AND S. HAMMARLING, A Schur method for the square root of a matrix, Linear Algebra Appl., 52/53 (1983), pp. 127-140.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 127-140
    • Bjorck, A.1    Hammarling, S.2
  • 4
    • 84966259249 scopus 로고
    • On the existence and uniqueness of the real logarithm of matrix
    • W. J. CULVER, On the existence and uniqueness of the real logarithm of matrix, Proc. Amer. Math. Soc., 17 (1966), pp. 1146-1151.
    • (1966) Proc. Amer. Math. Soc. , vol.17 , pp. 1146-1151
    • Culver, W.J.1
  • 5
    • 85033769933 scopus 로고    scopus 로고
    • Considerations on computing real logarithms of matrices, Hamiltonian logarithms, and skew-symmetric logarithms
    • to appear
    • L. DIECI, Considerations on computing real logarithms of matrices, Hamiltonian logarithms, and skew-symmetric logarithms, Linear Algebra Appl., to appear.
    • Linear Algebra Appl.
    • Dieci, L.1
  • 8
    • 84968481752 scopus 로고
    • Logarithms of matrices
    • B. W. HELTON, Logarithms of matrices, Proc. Amer. Math. Soc., 19 (1968), pp. 733-738.
    • (1968) Proc. Amer. Math. Soc. , vol.19 , pp. 733-738
    • Helton, B.W.1
  • 9
    • 0001485725 scopus 로고
    • Computing real square roots of a real matrix
    • N. J. HIGHAM, Computing real square roots of a real matrix, Linear Algebra Appl., 88/89 (1987), pp. 405-430.
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 405-430
    • Higham, N.J.1
  • 12
    • 0024738860 scopus 로고
    • Padé error estimates for the logarithm of a matrix
    • C. KENNEY AND A. J. LAUB, Padé error estimates for the logarithm of a matrix, International J. Control, 50-3 (1989), pp. 707-730.
    • (1989) International J. Control , vol.50 , Issue.3 , pp. 707-730
    • Kenney, C.1    Laub, A.J.2
  • 13
    • 0000831926 scopus 로고
    • Condition estimates for matrix functions
    • _, Condition estimates for matrix functions, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 191-209.
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 191-209
  • 14
    • 0019621372 scopus 로고
    • Transformation algorithm for identification of continuous-time multivariable systems from discrete data
    • G. J. LASTMAN AND N. K. SINHA, Transformation algorithm for identification of continuous-time multivariable systems from discrete data, Electron. Lett., 17 (1981), pp. 779-780.
    • (1981) Electron. Lett. , vol.17 , pp. 779-780
    • Lastman, G.J.1    Sinha, N.K.2
  • 15
    • 0026204075 scopus 로고
    • Infinite series for logarithm of matrix, applied to identification of linear continuous-time multivariable systems from discrete-time models
    • _, Infinite series for logarithm of matrix, applied to identification of linear continuous-time multivariable systems from discrete-time models, Electron. Lett., 27-16 (1991), pp. 1468-1470.
    • (1991) Electron. Lett. , vol.27 , Issue.16 , pp. 1468-1470
  • 16
    • 21844485402 scopus 로고
    • Condition estimation for matrix functions via the Schur decomposition
    • R. MATHIAS, Condition estimation for matrix functions via the Schur decomposition, SIAM J. Matrix Anal. Appl., 16-2 (1995), pp. 565-578.
    • (1995) SIAM J. Matrix Anal. Appl. , vol.16 , Issue.2 , pp. 565-578
    • Mathias, R.1
  • 17
  • 18
    • 0001143041 scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix
    • C. B. MOLER AND C. VAN LOAN, Nineteen dubious ways to compute the exponential of a matrix, SIAM Rev., 20 (1978), pp. 801-836.
    • (1978) SIAM Rev. , vol.20 , pp. 801-836
    • Moler, C.B.1    Van Loan, C.2
  • 19
    • 0000312029 scopus 로고
    • A recurrence among the elements of functions of triangular matrices
    • B. N. PARLETT, A recurrence among the elements of functions of triangular matrices, Linear Algebra Appl., 14 (1976), pp. 117-121.
    • (1976) Linear Algebra Appl. , vol.14 , pp. 117-121
    • Parlett, B.N.1
  • 20
    • 0039843998 scopus 로고
    • Note on real matrices and linear dynamical systems with periodic coefficients
    • Y. SIBUYA, Note on real matrices and linear dynamical systems with periodic coefficients, J. Math. Anal. Appl., 1 (1960), pp. 363-372.
    • (1960) J. Math. Anal. Appl. , vol.1 , pp. 363-372
    • Sibuya, Y.1
  • 21
    • 84925899548 scopus 로고
    • The representation of social processes by Markov models
    • B. SINGER AND S. SPILERMAN, The representation of social processes by Markov models, Amer. J. Sociology, 82-1 (1976), pp. 1-54.
    • (1976) Amer. J. Sociology , vol.82 , Issue.1 , pp. 1-54
    • Singer, B.1    Spilerman, S.2
  • 22
    • 0001884632 scopus 로고
    • HQR3 and EXCHNG: Fortran subroutines for calculating and ordering the eigenvalues of a real upper Hessenberg matrix
    • G. W. STEWART, HQR3 and EXCHNG: Fortran subroutines for calculating and ordering the eigenvalues of a real upper Hessenberg matrix, ACM Trans. Math. Software, 2 (1970), pp. 275-280.
    • (1970) ACM Trans. Math. Software , vol.2 , pp. 275-280
    • Stewart, G.W.1
  • 23
    • 0000509808 scopus 로고
    • The sensitivity of the matrix exponential
    • C. VAN LOAN, The sensitivity of the matrix exponential, SIAM J. Numer. Anal., 14 (1977), pp. 971-981.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 971-981
    • Van Loan, C.1
  • 24
    • 0026407341 scopus 로고
    • The matrix logarithm and the continuation of a discrete process
    • E. I. VERRIEST, The matrix logarithm and the continuation of a discrete process, in Proc. 1991 American Control Conference, 1991, pp. 184-189.
    • (1991) Proc. 1991 American Control Conference , pp. 184-189
    • Verriest, E.I.1
  • 26
    • 0001332750 scopus 로고
    • Numerical computation of the matrix exponential with accuracy estimates
    • R. C. WARD, Numerical computation of the matrix exponential with accuracy estimates, SIAM J. Numer. Anal., 14 (1977), pp. 600-610.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 600-610
    • Ward, R.C.1
  • 27
    • 0012737354 scopus 로고
    • Integral representation of the logarithm of matrices and operators
    • A. WOUK, Integral representation of the logarithm of matrices and operators, J. Math. Anal. Appl., 11 (1965), pp. 131-138.
    • (1965) J. Math. Anal. Appl. , vol.11 , pp. 131-138
    • Wouk, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.