Verified computation of the matrix exponential

Two numerical algorithms for computing interval matrices containing the matrix exponential are proposed. The first algorithm is based on a numerical spectral decomposition and requires only cubic complexity under some assumptions. The second algorithm is based on a numerical Jordan decomposition and...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 45; no. 1; pp. 137 - 152
Main Author Miyajima, Shinya
Format Journal Article
LanguageEnglish
Published New York Springer US 05.02.2019
Springer Nature B.V
Subjects
Algorithms
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Robustness (mathematics)
Visualization
Numerical Jordan decomposition
15A16
65F60
65G20
Verified numerical computation
Matrix exponential
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Summary:Two numerical algorithms for computing interval matrices containing the matrix exponential are proposed. The first algorithm is based on a numerical spectral decomposition and requires only cubic complexity under some assumptions. The second algorithm is based on a numerical Jordan decomposition and applicable even for defective matrices. Numerical results show the effectiveness and robustness of the algorithms.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-018-9609-5