On the Computation of Particular Eigenvectors of Hamiltonian Matrix Pencils

We discuss a structure‐preserving algorithm for the accurate solution of generalized eigenvalue problems for skew‐Hamiltonian/Hamiltonian matrix pencils λN − ℋ. By embedding the matrix pencil λ − ℋ into a skew‐Hamiltonian/Hamiltonian matrix pencil of double size it is possible to avoid the problem of non‐existence of a structured Schur form. For these embedded matrix pencils we can compute a particular condensed form to accurately compute the simple, finite, purely imaginary eigenvalues of λ − ℋ. In this paper we describe a new method to compute also the corresponding eigenvectors by using the information contained in the condensed form of the embedded matrix pencils and associated transformation matrices. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)