Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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.

23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg