Peter Benner, Vasile Sima, and Matthias Voigt

SLICOT Working Note 2013-2: August 2013.

Skew-Hamiltonian/Hamiltonian matrix pencils S - lambda H appear in many applications, including linear quadratic optimal control problems, H1-optimization, certain multi-body systems and many other areas in applied mathematics, physics, and chemistry. In these applications it is necessary to compute certain eigenvalues and/or corresponding deflating subspaces of these matrix pencils. Recently developed methods exploit and preserve the skew-Hamiltonian/Hamiltonian structure and hence increase reliability, accuracy and performance of the computations. In this paper we describe the implementation in SLICOT of the algorithms described in Part I of this work (see SLICOT Working Note 2013-1) and address various details. Furthermore, we perform numerical tests using real-world examples to demonstrate the superiority of the new algorithms compared to standard methods.