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.