Palindromic Polynomial Eigenvalue Problems:Good Vibrations from Good Linearizations
D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann · 2006
Abstract. Palindromic polynomial eigenvalue problems and related classes of structured eigenvalue problems are considered. These structures generalize the concepts of symplectic and Hamiltonian matrices to matrix polynomials. We discuss several applications where these matrix polynomials arise, and show how linearizations can be derived that reflect the structure of all these structured matrix polynomials and therefore preserve symmetries in the spectrum.