Numerische Mathematik

, Volume 143, Issue 3, pp 555–582 | Cite as

A structure preserving flow for computing Hamiltonian matrix exponential

  • Yueh-Cheng KuoEmail author
  • Wen-Wei Lin
  • Shih-Feng Shieh


This article focuses on computing Hamiltonian matrix exponential. Given a Hamiltonian matrix \(\mathcal {H}\), it is well-known that the matrix exponential \(e^{\mathcal {H}}\) is a symplectic matrix and its eigenvalues form reciprocal \((\lambda ,1/\bar{\lambda })\). It is important to take care of the symplectic structure for computing \(e^{\mathcal {H}}\). Based on the structure-preserving flow proposed by Kuo et al. (SIAM J Matrix Anal Appl 37:976–1001, 2016), we develop a numerical method for computing the symplectic matrix pair \((\mathcal {M},\mathcal {L})\) which represents \(e^{\mathcal {H}}\).

Mathematics Subject Classification

15A22 15A24 65F30 34A12 



We thank the Editor, Professor Volker Mehrmann, and the anonymous referees for their careful reading, valuable comments and suggestions on the manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational University of KaohsiungKaohsiungTaiwan
  2. 2.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan
  3. 3.Department of MathematicsNational Taiwan Normal UniversityTaipeiTaiwan

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