# 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)

## 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 MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theoryMSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis Dr Françoise Tisseur 19 Jun 2008 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/1109