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

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 is (non-Hermitian) system matrix has a positive definite semidefinite Hermitian part. In can solve iteratively by Krylov subspace methods based on efficient three-term recurrences. illustrate performance these iterative several examples. The be challenging requires additional techniques to deal with “singular part,” while “positive part” still treated recurrence methods.