On structured componentwise condition numbers for Hamiltonian eigenvalue problems

In this paper, we introduce the structured componentwise perturbation analysis to Hamiltonian eigenvalue problems. The explicit expressions for the relative structured componentwise condition number for Hamiltonian eigenvalue problems are derived. Also, we will compare the relative structured componentwise condition number with the relative unstructured componentwise condition number and the relative structured normwise condition number, respectively. We show the superiority of the relative structured componentwise condition number through numerical examples.