Numerical integration methods for Hamiltonian systems are of importance across many disciplines, including musical acoustics, where many systems of interest are very nearly lossless. Of particular interest are methods possessing a conserved pseu-doenergy. Though most such methods have an implicit character, an explicit method was proposed recently by Marazzato et al. The proposed method relies on a continuous integration which must be performed exactly in order for the conservation property to hold-as a result, it holds only approximately under numerical quadrature. Here, we show an explicit scheme for Hamiltonian integration, with a different choice of pseudoenergy, which is exactly conserved. Most importantly, a fast implementation is possible through the use of structured matrix inversion, and in particular Sherman Morrison inversion of the rank 1 perturbation of a matrix. Applications to the cases of fully nonlinear string vibration, and to the Föppl-von Kármán system describing large amplitude plate vibration are illustrated. Computation times are on par with the simplest non-conservative methods, such as Störmer integration
