The asymptotic analysis of the structure-preserving doubling algorithms

Abstract

This paper is the second part of [15]. Taking advantage of the special structure and properties of the Hamiltonian matrix, we apply a symplectically similar transformation introduced by [18] to reduce H to a Hamiltonian Jordan canonical form J. The asymptotic analysis of the structure-preserving flows and RDEs is studied by using eJt. The convergence of the SDA as well as its rate can thus result from the study of the structure-preserving flows. A complete asymptotic dynamics of the SDA is investigated, including the linear and quadratic convergence studied in the literature [3,12,13].