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Verified computation of the matrix exponential

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Abstract

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.

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Acknowledgements

The author acknowledges the referees for the valuable comments.

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Authors and Affiliations

  1. Faculty of Science and Engineering, Iwate University, 4-3-5 Ueda, Morioka-shi, Iwate, 020-8551, Japan

    Shinya Miyajima

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  1. Shinya Miyajima
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Correspondence to Shinya Miyajima.

Additional information

Communicated by: Peter Benner

This work was partially supported by JSPS KAKENHI Grant Number JP16K05270.

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Miyajima, S. Verified computation of the matrix exponential. Adv Comput Math 45, 137–152 (2019). https://doi.org/10.1007/s10444-018-9609-5

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  • DOI: https://doi.org/10.1007/s10444-018-9609-5

Keywords

Mathematics Subject Classification (2010)