## Skew-Hamiltonian and Hamiltonian Eigenvalue Problems: Theory, Algorithms and Applications

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Author(s) : Peter Benner , Daniel Kressner , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 44-2003

MSC 2000

65F15 Eigenvalues, eigenvectors

Abstract :
Skew-Hamiltonian and Hamiltonian eigenvalue problems arise from a number of applications, particularly in systems and control theory. The preservation of the underlying matrix structures often plays an important role in these applications and may lead to more accurate and more efficient computational methods. We will discuss the relation of structured and unstructured condition numbers for these problems as well as algorithms exploiting the given matrix structures. Applications of Hamiltonian and skew-Hamiltonian eigenproblems are briefly described.

Keywords : Hamiltonian matrix, skew-Hamiltonian matrix, structured condition numbers, structure-preserving algorithms