On Non-Hermitian Positive (Semi)Definite Linear Algebraic Systems Arising from Dissipative Hamiltonian DAEs

Authors

Candan Güdücü, Jörg Liesen, Volker Mehrmann, Daniel B. Szyld

Abstract

We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For each case we give examples from practical applications. An important feature of the linear algebraic systems is that the (non-Hermitian) system matrix has a positive definite or semidefinite Hermitian part. In the positive definite case we can solve the linear algebraic systems iteratively by Krylov subspace methods based on efficient three-term recurrences. We illustrate the performance of these iterative methods on several examples. The semidefinite case can be challenging and requires additional techniques to deal with”singular part”, while the”positive definite part”can still be treated with the three-term recurrence methods.

Citation

• Journal: SIAM Journal on Scientific Computing
• Year: 2022
• Volume: 44
• Issue: 4
• Pages: A2871–A2894
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• DOI: 10.1137/21m1458594

BibTeX

@article{G_d_c__2022,
  title={{On Non-Hermitian Positive (Semi)Definite Linear Algebraic Systems Arising from Dissipative Hamiltonian DAEs}},
  volume={44},
  ISSN={1095-7197},
  DOI={10.1137/21m1458594},
  number={4},
  journal={SIAM Journal on Scientific Computing},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Güdücü, Candan and Liesen, Jörg and Mehrmann, Volker and Szyld, Daniel B.},
  year={2022},
  pages={A2871--A2894}
}

Download the bib file

References

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