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Mackey, D.S., Mackey, N., Mehl, C. and Mehrmann, V. (2005) Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations. Technical Report 239, DFG Research Center Matheon, Mathematics for Key Technologies, Berlin.

has been cited by the following article:

• 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.