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Numerical Methods for Eigenvalue and Control Problems

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Frontiers in Numerical Analysis

Part of the book series: Universitext ((UTX))

Abstract

We briefly survey some of the classical methods for the numerical solution of eigenvalue problems, including methods for large scale problems. We also briefly discuss some of the basics of linear control theory, including stabilization and optimal control and show how they lead to several types of eigenvalue problems. We then discuss how these problems from control theory can be solved via classical and also nonclassical eigenvalue methods. The latter include recently developed structure preserving methods for the solution of Hamiltonian eigenvalue problems. We also demonstrate how structured eigenvalue methods can be developed for large scale and polynomial eigenvalue problems.

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Author information

Authors and Affiliations

  1. Institut für Mathematik MA 4-5, Technische Universität Berlin, Str. des 17. Juni 136, D-10623, Berlin, Germany

    Volker Mehrmann

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  1. Volker Mehrmann
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Editors and Affiliations

  1. Department of Mathematical Sciences, University of Durham, South Road, DH1 3LE, Durham, UK

    James F. Blowey  & Alan W. Craig  & 

  2. Department of Mathematics, University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Tony Shardlow

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Mehrmann, V. (2003). Numerical Methods for Eigenvalue and Control Problems. In: Blowey, J.F., Craig, A.W., Shardlow, T. (eds) Frontiers in Numerical Analysis. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55692-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-55692-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44319-3

  • Online ISBN: 978-3-642-55692-0

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