# 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…

## 3 Citations

Global symplectic Lanczos method with application to matrix exponential approximation

- Mathematics
- 2021

It is well-known that the symplectic Lanczos method is an efficient tool for computing a few eigenvalues of large and sparse Hamiltonian matrices. A variety of block Krylov subspace methods were…

A block J-Lanczos method for Hamiltonian matrices

- Mathematics
- 2020

This work aims to present a structure-preserving block Lanczos-like method. The Lanczos-like algorithm is an effective way to solve large sparse Hamiltonian eigenvalue problems. It can also be used…

Krylov projection methods for linear Hamiltonian systems

- Computer Science, MathematicsNumerical Algorithms
- 2019

The connection to structure preserving model reduction is discussed and the performance of Krylov projection methods is illustrated by applying them to Hamiltonian PDEs.

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