2021/11/10 by Candan Güdücü, Güdücü, Candan, Jörg Liesen +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #65F10 #65L80 #93A15 #93B11 #93B15 #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2111.05616
openalex publication_date 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.