Volume 8, pp. 115-126, 1999.

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

Peter Benner, Volker Mehrmann, and Hongguo Xu


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.

Full Text (PDF) [110 KB], BibTeX

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

ETNA articles which cite this article

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
Vol. 58 (2023), pp. 402-431 Tim Mitchell: Fast computation of Sep$_\lambda$ via interpolation-based globality certificates

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