A BLOCK J-LANCZOS METHOD FOR HAMILTONIAN MATRICES

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 to approximate exp(A) V for a given large square matrix A and a tall-and-skinny matrix V such that the geometric property of V is preserved, which interests us in this paper. This approximation is important for solving systems of ordinary differential equations (ODEs) or time-dependent partial differential equations (PDEs). Our approach is based on a block J-tridiagonalization procedure of a Hamiltonian and skew-symmetric matrix using symplectic similarity transformations.