Krylov integrators for Hamiltonian systems

@article{Eirola2018KrylovIF,
  title={Krylov integrators for Hamiltonian systems},
  author={Timo Eirola and Antti Koskela},
  journal={BIT Numerical Mathematics},
  year={2018},
  volume={59},
  pages={57-76}
}
We consider Arnoldi-like processes to obtain symplectic subspaces for Hamiltonian systems. Large dimensional systems are locally approximated by ones living in low dimensional subspaces, and we especially consider Krylov subspaces and some of their extensions. These subspaces can be utilized in two ways: by solving numerically local small dimensional systems and then mapping back to the large dimension, or by using them for the approximation of necessary functions in exponential integrators… 

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