The Padé method for computing the matrix exponential

Linear Algebra and Its Applications

Volumn 240, Issue , 1996, Pages 111-130

  Arioli, M ^a   Codenotti, B ^b   Fassino, C ^c  

^a CNR   (Italy)

^b CNR Consiglio Nazionale delle Ricerche   (Italy)

^c UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21344447916     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/0024-3795(94)00190-1     Document Type: Article

References (13)

1. C. Fassino, Computation of matrix function, Ph.D. Thesis, Univ. of Pisa, 1993.
2. A. F. Fath, Evaluation of a matrix polynomial, IEEE Trans. Automat. Control AC-13:220-221 (1968).
3. G. H. Golub and C. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins U. P., Baltimore, 1989.
4. J. L. Howland, Further ways to approximate the exponential of a matrix, Linear and Multilinear Algebra 14:121-129 (1983).
5. C. Moler and C. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, SIAM Rev. 14:801-836 (1978).
6. L. F. Shampine and M. K. Gordon, Computer Solution of Ordinary Differential Equations - The Initial Value Problem, Freeman, San Francisco, 1975.
7. R. D. Skeel, Iterative refinement implies numerical stability for Gaussian elimination, Math. Comp. 35:817-832 (1980).
8. C. J. Standish, Truncated Taylor series approximation to the state transition matrix of a continuous parameter finite Markov chain, Linear Algebra Appl. 12:179-183 (1975).
9. C. Van Loan, On the limitation and application of Padé approximation to matrix exponential, in Padé and Rational Approximation, Academic, 1977, pp. 439-448.
10. _, A note on the evaluation of matrix polynomials, IEEE Trans. Automat. Control AC-24:320-321 (1979).
11. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962.
12. R. C. Ward, Numerical computation of the matrix exponential with accuracy estimate, SIAM J. Numer. Anal. 14:600-610 (1977).
13. G. Birkhoff and R. S. Varga, Reactor criticality and non-negative matrices, J. Soc. Industr. Appl. Math. 6:354-377 (1958).