Open AccessAn extended Hessenberg form for Hamiltonian matrices
Author(s) -
Micol Ferranti,
Bruno Iannazzo,
Thomas Mach,
Raf Vandebril
Publication year - 2016
Publication title -
calcolo
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.876
H-Index - 33
eISSN - 1126-5434
pISSN - 0008-0624
DOI - 10.1007/s10092-016-0192-1
Subject(s) - mathematics , linear subspace , hamiltonian (control theory) , symplectic geometry , hamiltonian path problem , superintegrable hamiltonian system , hamiltonian system , algebra over a field , covariant hamiltonian field theory , pure mathematics , mathematical analysis , discrete mathematics , hamiltonian path , mathematical optimization , graph
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
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