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| Abstract: Skew-Hamiltonian/Hamiltonian matrix pencils λS - H appear in many applications including linear quadratic optimal control problems H∞-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 which have been implemented in the style of subroutines of 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. |
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