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. Most of this paper was originally published in 1978. An update, with a separate bibliography, describes a few recent developments.
Keywords
Eigenvalues and eigenvectorsMatrix exponentialMatrix (chemical analysis)MathematicsApplied mathematicsExponential functionMatrix differential equationPolynomial matrixDifferential equationMatrix polynomialAlgebra over a fieldPolynomialCalculus (dental)Mathematical analysisPure mathematicsMedicinePhysics
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Publication Info
- Year
- 2003
- Type
- article
- Volume
- 45
- Issue
- 1
- Pages
- 3-49
- Citations
- 2315
- Access
- Closed
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Cite This
C Moler,
Charles Van Loan
(2003).
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later.
SIAM Review
, 45
(1)
, 3-49.
https://doi.org/10.1137/s00361445024180
Identifiers
- DOI
- 10.1137/s00361445024180