Perturbation analysis of Hamiltonian Schur and Block-Schur forms (Q2784353)

In Section 2 of this paper the authors consider three condensed forms: Hamiltonian Schur form, Hamiltonian block-Schur form and block-Schur form under similarity transformations, for Hamiltonian matrices under the similarity action of the unitary symplectic and unitary transformation groups, respectively. In Section 3, they formulate the basic problems in the perturbation analysis for the three forms. In Section 4 they derive basic relations necessary for the perturbation analysis of the three condensed forms described in Sections 2 and 3.NEWLINENEWLINENEWLINEIn Section 5, they present a detailed first order (or asymptotic) perturbation analysis of the condensed forms for Hamiltonian matrices, giving the first order terms of the corresponding perturbation bounds. In Section 6 they derive nonlinear, nonlocal perturbation bounds for the condensed forms. In Section 7, they show a different way to obtain nonlinear perturbation bounds for the condensed forms of Hamiltonian matrices based on power series expansions for the perturbations in the condensed forms of Hamiltonian matrices.NEWLINENEWLINENEWLINEIn Section 8, they present a numerical example which illustrates the accuracy and applicability of the derived linear and nonlinear perturbation bounds for the Hamiltonian Schur form.