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On the Computation of Particular Eigenvectors of Hamiltonian Matrix Pencils
Author(s) -
Benner Peter,
Voigt Matthias
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110366
Subject(s) - matrix pencil , eigenvalues and eigenvectors , hamiltonian matrix , mathematics , skew , embedding , hamiltonian (control theory) , eigendecomposition of a matrix , pencil (optics) , skew symmetric matrix , pure mathematics , algebra over a field , symmetric matrix , physics , computer science , quantum mechanics , square matrix , mathematical optimization , astronomy , artificial intelligence
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)