Author(s)

Mustapha Bassour^1,2

¹Faculté des Sciences Juridiques, Economiques et Sociales, Ait Melloul, Morocco.
²LISTI Laboratory ENSA, Ibn Zohr University, Agadir, Morocco.

We present in this paper a new method for solving polynomial eigenvalue problem. We give methods that decompose a skew-Hamiltonian matrix using Cholesky like-decomposition. We transform first the polynomial eigenvalue problem to an equivalent skew-Hamiltonian/Hamiltonian pencil. This process is known as linearization. Decomposition of the skew-Hamiltonian matrix is the fundamental step to convert a structured polynomial eigenvalue problem into a standard Hamiltonian eigenproblem. Numerical examples are given.

Hamiltonian Matrix, Polynomial Eigenvalue Problem, Skew-Hamiltonian/Hamiltonian Pencil, Cholesky Like-Decomposition

Bassour, M. (2020) Hamiltonian Polynomial Eigenvalue Problems. Journal of Applied Mathematics and Physics, 8, 609-619. doi: 10.4236/jamp.2020.84047.