TITLE:
Hamiltonian Polynomial Eigenvalue Problems
AUTHORS:
Mustapha Bassour
KEYWORDS:
Hamiltonian Matrix, Polynomial Eigenvalue Problem, Skew-Hamiltonian/Hamiltonian Pencil, Cholesky Like-Decomposition
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.4,
March
31,
2020
ABSTRACT: 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.