A structure preserving flow for computing Hamiltonian matrix exponential

Abstract

This article focuses on computing Hamiltonian matrix exponential. Given a Hamiltonian matrix H, it is well-known that the matrix exponential e(H) is a symplectic matrix and its eigenvalues form reciprocal (lambda, 1/(lambda) over bar). It is important to take care of the symplectic structure for computing e(H). Based on the structure-preserving flow proposed by Kuo et al. (SIAM J Matrix Anal Appl 37:976-1001, 2016), we develop a numerical method for computing the symplectic matrix pair (M, L) which represents e(H).