Numerical methods for palindromic eigenvalue problems: Computing the anti‐triangular Schur form
D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann · Numerical Linear Algebra with Applications · 2008
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 ±1, are discussed. We show how a combination of unstructured methods followed by a structured refinement can be used to solve such problems accurately. Copyright © 2008 John Wiley & Sons, Ltd.