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Nineteen Dubious Ways to Compute the Exponential of a Matrix
Abstract
In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficiency indicates that some of the methods are preferable to others, but that none are completely satisfactory.
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Citations
Cites
On the product of semi-groups of operators
Trotter, H. F. (1959) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1959-0108732-6 · Cited by 2,282
Cited by
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Minh, B. Q., Schmidt, H. A., Chernomor, O., Schrempf, D., Woodhams, M. D., von Haeseler, A., & Lanfear, R. (2020) · Molecular Biology and Evolution · doi:10.1093/molbev/msaa015 · Cited by 16,873
(1994) · Molecular Biology and Evolution · doi:10.1093/oxfordjournals.molbev.a040152 · Cited by 920
Expokit: a software package for computing matrix exponentials
Sidje, R. B. (1998) · ACM Transactions on Mathematical Software · doi:10.1145/285861.285868 · Cited by 781
Quantum mechanical optimal control of physical observables in microsystems
Shi, S., & Rabitz, H. (1990) · The Journal of Chemical Physics · doi:10.1063/1.458438 · Cited by 323
Efficient Solution of Parabolic Equations by Krylov Approximation Methods
Gallopoulos, E., & Saad, Y. (1992) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0913071 · Cited by 320
Metadata
- Authors
- Moler, C., & Van Loan, C.
- Venue
- SIAM Review
- Published
- 1978-10
- Volume
- 20
- Issue
- 4
- Pages
- 801-836
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2067136705
- Cited by
- 1,526
- References
- 1
- FWCI
- 16.61
- Type
- journal article
- Language
- en
- Open access
- closed
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