## A note on the numerical solution of complex Hamiltonian and skew-Hamiltonian eigenvalue problems

Peter Benner, Volker Mehrmann, and Hongguo Xu

### Abstract

In this paper we describe a simple observation that can be used to extend two recently proposed structure preserving methods for the eigenvalue problem for real Hamiltonian matrices to the case of complex Hamiltonian and skew-Hamiltonian matrices.

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### Key words

eigenvalue problem, Hamiltonian matrix, skew-Hamiltonian matrix, algebraic Riccati equation, invariant subspace.

### AMS subject classifications

65F15, 93B40, 93B36, 93C60.

### Links to the cited ETNA articles

 [1] Vol. 1 (1993), pp. 33-48 Gregory Ammar, Peter Benner, and Volker Mehrmann: A multishift algorithm for the numerical solution of algebraic Riccati equations

 Vol. 26 (2007), pp. 121-145 H. Faßbender: The parametrized $SR$ algorithm for Hamiltonian matrices Vol. 55 (2022), pp. 455-468 Chen Greif: Structured shifts for skew-symmetric matrices