Choosing the best approach to matrix exponentiation

Computers and Operations Research

Volumn 26, Issue 9, 1999, Pages 871-882

  Vanden Bosch, Peter M ^a   Dietz, Dennis C ^a,b   Pohl, Edward A ^a  

^a AIR FORCE INSTITUTE OF TECHNOLOGY   (United States)

^b US West Advanced Technologies   (United States)

Author keywords

Catastrophic cancellation; Matrix exponentiation; Transition matrix

Indexed keywords

DIGITAL ARITHMETIC; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; MATRIX ALGEBRA; PRECISION ENGINEERING;

MATRIX EXPONENTIATION;

OPERATIONS RESEARCH;

COMPUTER SYSTEM; METHODOLOGY;

EID: 0033179539     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0305-0548(98)00097-5     Document Type: Article

References (14)

1. Moler C, Van Loan CF. Nineteen dubious ways to compute the exponential of a matrix. SIAM Review 1978;20:801-37.
2. Vanden Bosch PM. Scheduling and Sequencing Arrivals to a Stochastic Service System. PhD dissertation, Air Force Institute of Technology, 1997.
3. Golub GH, Van Loan CF. Matrix Computations. Baltimore: Johns-Hopkins University Press, 1989.
4. Lin YY, Hwang LP. Efficient computation of the matrix exponential using Padé approximation. Computers in Chemistry 1989;10:285-93.
5. Moler C. Personal Correspondence. Natick, MA, 21-23 September, 1996.
6. Van Loan CF. On the limitation and application of the Padé approximation to the matrix exponential. In: Saff EB, Varga RS, editors, Padé and Rational Approximation. New York: Academic Press, 1977.
7. Ward RC. Numerical computation of the matrix exponential with accuracy estimate. SIAM Journal on Numerical Analysis 1977;14:600-14.
8. Gray WJ, Wang PP. On the computation of optimal arrival times for a single-server system. Chinese Institute of Industrial Engineering 1995;14:245-52.
9. Bronson R. Theory and Problems of Matrix Exponentiation. New York: McGraw-Hill, 1989.
10. Parlett RN. A recurrence among the elements of functions of triangular matrices. Linear Algebra and its Applications 1976;14:117-21.
11. Parlett RN. Computation of Functions of Triangular Matrices. Working Paper ERL-M481. Electronics Research Laboratory, University of California, Berkeley, 1974.
12. Liou ML. A novel method of evaluating transient response. Proceedings of the IEEE 1966;54:20-3.
13. Standish CJ. Truncated taylor series approximation to the state transition matrix of a continuous parameter finite Markov chain. Linear Algebra and its Applications 1975;12:179-83.
14. Bryant V. Metric Spaces: Iteration and Application. Cambridge: Cambridge University Press, 1985.