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