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01-06-2016

An extended Hessenberg form for Hamiltonian matrices

Authors: Micol Ferranti, Bruno Iannazzo, Thomas Mach, Raf Vandebril

Published in: Calcolo | Issue 1/2017

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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.

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The name extended refers to the link with extended Krylov subspaces, see [12] for details.

If the matrix exhibits particular structure, core transformations could equal the identity and are therefore not shown in the pyramidal structure.

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Title: An extended Hessenberg form for Hamiltonian matrices
Authors: Micol Ferranti
Bruno Iannazzo
Thomas Mach
Raf Vandebril
Publication date: 01-06-2016
Publisher: Springer Milan
Published in: Calcolo / Issue 1/2017
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-016-0192-1

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