An extended Hessenberg form for Hamiltonian matrices
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Date
2016-06-01
Authors
Ferranti, Micol
Iannazzo, Bruno
Mach, Thomas
Vandebril, Raf
Journal Title
Journal ISSN
Volume Title
Publisher
Calcolo
Abstract
A unitary symplectic similarity transformation for a special class of Hamiltonian matrices to extended Hamiltonian Hessenberg form is presented. Whereas the classical Hessenberg form links to Krylov subspaces, the extended Hessenberg form links to extended Krylov subspaces. The presented algorithm generalizes thus the classic reduction to Hamiltonian Hessenberg form and offers more freedom in the choice of Hamiltonian condensed forms, to be used within an extended Hamiltonian QR algorithm. Theoretical results identifying the structure of the extended Hamiltonian Hessenberg form and proofs of uniqueness of the reduction process are included. Numerical experiments confirm the validity of the approach.
Description
Keywords
extended hessenberg forms, hamiltonian eigenvalue problems, QR algorithm
Citation
Ferranti, M., Iannazzo, B., Mach, T., & Vandebril, R. (2016). An extended Hessenberg form for Hamiltonian matrices. Calcolo, 1-31. DOI: 10.1007/s10092-016-0192-1