POLYNOMIAL EIGENVALUE PROBLEMS WITH HAMILTONIAN STRUCTURE

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A numerical method for polynomial eigenvalue problems using contour integral (2010, background): “We consider the quartic eigenvalue problem F (λ) = λ(4)A4 + λ (3)A3 + λ (2)A2 + λA1 + A0, given in [14].”
NLEVP: A Collection of Nonlinear Eigenvalue Problems (2013, methodology): “This is a quartic matrix polynomial P (λ) = λ(4)A4 +λ (2)A3 +λ (2)A2 +λA1 +A0 of dimension m 2 with T-even structure, depending on a 10×1 parameter vector c [35].”
An Arnoldi Method for Nonlinear Eigenvalue Problems (2004, unknown): “[8, 9]).”
Jordan structures of alternating matrix polynomials (2010, background): “Conditions when it is possible to find a T -even or T -odd linearization were investigated in [20, 23].”
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations (2006, background): “Higher order * -even eigenvalue problems arise in the linear quadratic optimal control problem for higher order systems of ordinary differential equations [33].”
Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods (2004, methodology): “These methods are able to deal with most of the small or large scale problems in practice [1, 6, 16, 53, 58] and specific methods have been developed to handle extra structures [9, 12, 61, 63, 64].”