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## 2008.60: Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form

2008.60: D. Steven Mackey, Niloufer Mackey, Christian Mehl and Volker Mehrmann (2007) Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form. Numerical Linear Algebra with Applications.

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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 MSC 2000 > 15 Linear and multilinear algebra; matrix theoryMSC 2000 > 65 Numerical analysis 2008.60 Dr Françoise Tisseur 19 June 2008