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Volumn 30, Issue 4, 2008, Pages 1639-1657

Computing the fréchet derivative of the matrix exponential, with an application to condition number estimation

Author keywords

Backward error analysis; Condition number estimation; Fr chet derivative; Matrix exponential; Matrix function; Matrix iteration; Matrix polynomial; Pad approximation; Scaling and squaring method

Indexed keywords

BACKWARD ERROR ANALYSIS; CONDITION NUMBER ESTIMATION; MATRIX EXPONENTIAL; MATRIX FUNCTION; MATRIX ITERATION; MATRIX POLYNOMIAL; SCALING AND SQUARING METHOD;

EID: 70449440430     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/080716426     Document Type: Article
Times cited : (90)

References (17)
  • 5
    • 27144549311 scopus 로고    scopus 로고
    • The scaling and squaring method for the matrix exponential revisited
    • N. J. Higham, The scaling and squaring method for the matrix exponential revisited, SIAM J. Matrix Anal. Appl., 26 (2005), pp. 1179-1193.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , pp. 1179-1193
    • Higham, N.J.1
  • 6
    • 70449395396 scopus 로고    scopus 로고
    • Functions of matrices: Theory and computation
    • Philadelphia, PA
    • N. J. Higham, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, PA, 2008.
    • (2008) SIAM
    • Higham, N.J.1
  • 7
    • 0034144755 scopus 로고    scopus 로고
    • A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra
    • N. J. Higham and F. Tisseur, A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1185-1201.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 1185-1201
    • Higham, N.J.1    Tisseur, F.2
  • 8
    • 17644412903 scopus 로고    scopus 로고
    • Computing estimates of continuous time macroeconometric models on the basis of discrete data
    • G. Jewitt and J. R. McCrorie, Computing estimates of continuous time macroeconometric models on the basis of discrete data, Comput. Statist. Data Anal., 49 (2005), pp. 397-416.
    • (2005) Comput. Statist. Data Anal. , vol.49 , pp. 397-416
    • Jewitt, G.1    McCrorie, J.R.2
  • 9
    • 0000831926 scopus 로고
    • Condition estimates for matrix functions
    • C. S. Kenney and A. J. Laub, 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
    • Kenney, C.S.1    Laub, A.J.2
  • 10
    • 0001537596 scopus 로고
    • Polar decomposition and matrix sign function condition estimates
    • C. S. Kenney and A. J. Laub, Polar decomposition and matrix sign function condition estimates, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 488-504.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 488-504
    • Kenney, C.S.1    Laub, A.J.2
  • 11
    • 0032371908 scopus 로고    scopus 로고
    • A Schur-Fréchet algorithm for computing the logarithm and exponential of a matrix
    • C. S. Kenney and A. J. Laub, A Schur-Fréchet algorithm for computing the logarithm and exponential of a matrix, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 640-663.
    • (1998) SIAM J. Matrix Anal. Appl. , vol.19 , pp. 640-663
    • Kenney, C.S.1    Laub, A.J.2
  • 12
    • 21144461849 scopus 로고
    • Evaluating the Frechet derivative of the matrix exponential
    • R. Mathias, Evaluating the Frechet derivative of the matrix exponential, Numer. Math., 63 (1992), pp. 213-226.
    • (1992) Numer. Math. , vol.63 , pp. 213-226
    • Mathias, R.1
  • 13
    • 0030519908 scopus 로고    scopus 로고
    • A chain rule for matrix functions and applications
    • R. Mathias, A chain rule for matrix functions and applications, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 610-620.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 610-620
    • Mathias, R.1
  • 14
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • C. B. Moler and C. F. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45 (2003), pp. 3-49.
    • (2003) SIAM Rev. , vol.45 , pp. 3-49
    • Moler, C.B.1    Van Loan, C.F.2
  • 15
    • 0001518003 scopus 로고
    • Derivatives of the matrix exponential and their computation
    • I. Najfeld and T. F. Havel, Derivatives of the matrix exponential and their computation, Adv. Appl. Math., 16 (1995), pp. 321-375.
    • (1995) Adv. Appl. Math. , vol.16 , pp. 321-375
    • Najfeld, I.1    Havel, T.F.2
  • 16
    • 0002534227 scopus 로고
    • On the number of nonscalar multiplications necessary to evaluate polynomials
    • M. S. Paterson and L. J. Stockmeyer, On the number of nonscalar multiplications necessary to evaluate polynomials, SIAM J. Comput., 2 (1973), pp. 60-66.
    • (1973) SIAM J. Comput. , vol.2 , pp. 60-66
    • Paterson, M.S.1    Stockmeyer, L.J.2
  • 17
    • 0001332750 scopus 로고
    • Numerical computation of the matrix exponential with accuracy estimate
    • R. C. Ward, Numerical computation of the matrix exponential with accuracy estimate, SIAM J. Numer. Anal., 14 (1977), pp. 600-610.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 600-610
    • Ward, R.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.