# On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs

@article{Gdc2021OnNP, title={On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs}, author={Candan G{\"u}d{\"u}c{\"u} and J{\"o}rg Liesen and Volker Mehrmann and Daniel B. Szyld}, journal={ArXiv}, year={2021}, volume={abs/2111.05616} }

. 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…

## 3 Citations

### A flexible short recurrence Krylov subspace method for matrices arising in the time integration of port Hamiltonian systems and ODEs/DAEs with a dissipative Hamiltonian

- Computer ScienceArXiv
- 2022

New, right preconditioned variants of this approach which as their crucial new feature allow the systems with the Hermitian part to be solved only approximately in each iteration while keeping the short recurrences.

### A Rosenbrock framework for tangential interpolation of port-Hamiltonian descriptor systems

- Computer ScienceArXiv
- 2022

A new structure-preserving model order reduction (MOR) framework for large-scale port-Hamiltonian descriptor systems (pH-DAEs) is presented, which produces reduced-order models (ROMs) of minimal dimension, which tangentially interpolate the original model’s transfer function and are guaranteed to be again in pH-DAE form.

### Structure-Preserving Model Order Reduction for Index Two Port-Hamiltonian Descriptor Systems

- Computer ScienceArXiv
- 2022

This work develops optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian descriptor systems of differentiation index one that include a simplified treatment of algebraic constraints and often a higher accuracy of the resulting reduced-order model.

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