An Implicitly Symplectic Lanczos Algorithm for Hamiltonian Matrices

Abstract

The purpose of this paper is to outline a structure-preserving Lanczos-type algorithm, named implicitly symplectic Lanczos algorithm for real Hamiltonian matrices. The algorithm is based on a symplectic reduction procedure of Hamiltonian matrix using symplectic similarity transformations with symplectic reflectors defined on R2n×2. Numerical results for the proposed algorithm are treated.