Lu, Z.J., van der Vegt, J.J.W. and Xu, Y. (2018) Spectral Approximation for Polynomial Eigenvalue Problems. Computers and Mathematics with Applications, 76, 1184-1197.
https://doi.org/10.1016/j.camwa.2018.06.007

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.