Cited by 2,357Matrix Theory and AlgorithmsNumerical Methods and AlgorithmsNumerical methods for differential equations

Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later

Moler, Cleve, Van Loan, Charles·2003·SIAM Review

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.

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Crossref · 10.1137/s00361445024180

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127 of 127 references verified0 citation errors · 0 not checkable

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  • In the interaction picture, the time evolution of the system is shared between the density matrix and other operators.

    “In the interaction picture, the time evolution of the system is shared between the density matrix and other operators [37, 38].”

    From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [37]

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Authors
Moler, C., & Van Loan, C.
Affiliations
MathWorks (United Kingdom) (GB)
Venue
SIAM Review
Published
2003-01
Volume
45
Issue
1
Pages
3-49
ISSN
  • 0036-1445 (ISSN-L)
  • 1095-7200
OpenAlex
W2106565812
Cited by
2,357
References
127
Citations by year
2026: 67 · 2025: 98 · 2024: 115 · 2023: 82 · 2022: 99 · 2021: 124 · 2020: 135 · 2019: 144 · 2018: 136 · 2017: 161 · 2016: 129 · 2015: 127 · 2014: 161 · 2013: 114 · 2012: 108
FWCI
44.44
Type
journal article
Language
en
Open access
closed
Locations
SIAM Review (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
  • Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
Keywords
matrix exponential, numerical stability, computational efficiency, approximation theory, differential equations, matrix eigenvalues, characteristic polynomial

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