Peter Benner, Vasile Sima, and Matthias Voigt

SLICOT Working Note 2013-1: 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 corresponding algorithms whose implementations have been included in the Subroutine Library in Control Theory (SLICOT). Furthermore we address some of their applications. We describe variants for real and complex problems with versions for factored and unfactored matrices S.