Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form

Mackey, D. Steven and Mackey, Niloufer and Mehl, Christian and Mehrmann, Volker (2007) Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form. Numerical Linear Algebra with Applications. (In Press)

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Abstract

We present structure-preserving numerical methods for the eigenvalue problem of complex palindromic pencils. Such problems arise in control theory, as well as from palindromic linearizations of higher degree palindromic matrix polynomials. A key ingredient of these methods is the development of an appropriate condensed form --- the anti-triangular Schur form. Ill-conditioned problems with eigenvalues near the unit circle, in particular near $\pm 1$, are discussed. We show how a combination of unstructured methods followed by a structured refinement can be used to solve such problems accurately.

Item Type: Article
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Fran├žoise Tisseur
Date Deposited: 19 Jun 2008
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1109

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