FORTRAN 77 subroutines for the solution of Skew-Hamiltonian/Hamiltonian eigenproblems / Peter Benner, Vasile Sima, Matthias Voigt

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870495151

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urn:nbn:de:gbv:3:2-64250

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Benner, Peter
Sima, Vasile
Voigt, Matthias

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Max-Planck-Institut für Dynamik Komplexer Technischer Systeme

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Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, 2013-

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1 Online-Ressource

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eng

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Item type:Monographie of multivolume work,
Algorithms and applications / Peter Benner, Vasile Sima, Matthias Voigt
(Max Planck Institute for Dynamics of Complex Technical Systems) Benner, Peter; Sima, Vasile; Voigt, Matthias; Max-Planck-Institut für Dynamik Komplexer Technischer Systeme
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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Item type:Monographie of multivolume work,
Implementation and numerical results / Peter Benner, Vasile Sima, Matthias Voigt
(Max Planck Institute for Dynamics of Complex Technical Systems) Benner, Peter; Sima, Vasile; Voigt, Matthias; Max-Planck-Institut für Dynamik Komplexer Technischer Systeme
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 implementation of the algorithms in the style of subroutine included in the Subroutine Library in Control Theory (SLICOT) described in Part I of this work 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.

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