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

  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},
. 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… 

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A Generalization of the Hermitian and Skew-Hermitian Splitting Iteration

  • M. Benzi
  • Mathematics
    SIAM J. Matrix Anal. Appl.
  • 2009
It is shown that the new scheme can outperform the standard HSS method in some situations and can be used as an effective preconditioner for certain linear systems in saddle point form.