Structure Preserving Algorithm for the Logarithm of Symplectic Matrices

The current algorithms use either the full form or Schur decomposition of matrix in inverse scaling and squaring method to compute logarithm. consists two main calculations: taking a square root evaluating Padé approximants. In this work, we suggest using structure preserving iteration as an alternative Denman-Beavers for root. Numerical experiments show that while preserves Hamiltonian logarithm, cause loss.