A structure preserving approximation method for Hamiltonian exponential matrices

The approximation of exp(A)V where A is a real matrix and V a rectangular matrix is the key ingredient of many exponential integrators for solving systems of ordinary differential equations. In this paper we give an appropriate structure preserving approximation method to exp(A)V when A is a Hamiltonian or skew-Hamiltonian 2n-by-2n real matrix. Our approach is based on Krylov subspace methods that preserve Hamiltonian or skew-Hamiltonian structure. In this regard we use a symplectic Lanczos algorithm to compute the desired approximation.