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Linear Algebra for Control Theory pp 87–102Cite as

On the Rutishauser’s Approach to Eigenvalue Problems

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 62))

Abstract

We consider the quotient-difference algorithm of H. Rutishauser from the point of view of the realization theory of rational functions. QR-like algorithms of the linear algebra can be thought of as discrete-time dynamical systems on certain classes of matrices. We show that these algorithms induce linear dynamical systems on various manifolds of rational functions. Applications to coding theory are considered.

This work was partially supported by NSF through IMA grant.

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References

  1. A. Bunse-Gerstner. An analysis of the HR-algorithm for computing the eigenvalues of a matrix. Linear Algebra and its Applications, 35 (1981), pp. 155–173.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Brockett and L. Faybusovich. Toda flows, inverse spectral transform and realization theory. Systems and Control Letters, 16 (1991), pp. 79–88.

    Article  MathSciNet  MATH  Google Scholar 

  3. L. Faybusovich. Hamiltonian and system-theoretic properties of the HR-algorithm. (to appear in Journal of Mathematical Systems, Estimation and Control).

    Google Scholar 

  4. P. Henrici. Applied and Computational complex analysis. Vol. 1, John Willey & Sons, 1974.

    MATH  Google Scholar 

  5. R. Lidl and H. Niederreiter. Introduction to finite fields and their applications. Cambridge University Press, 1985.

    Google Scholar 

  6. J. Moser. Finitely many points on the line under the influence of an exponential potential — an integrable system. In: J. Moser, Ed. Dynamical Systems, Theory and Applications, Lecture Notes in Physics, Vol. 38 (1975), pp. 467–497.

    Chapter  Google Scholar 

  7. H. Rutishauser. Anwendunger des Quotienten — Differenzen — Algorithmus. ZAMP, 5 (1954), pp. 496–508.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. Rutishauser. Eir infinitesimales Analogon zum Quotienten — Differenzen — Algorithmus. Arch. Math. 5 (1984), pp. 132–137.

    Article  MathSciNet  Google Scholar 

  9. D. Watkins. Fundamentals of matrix computations. John Willey & Sons, 1991.

    MATH  Google Scholar 

  10. D. Watkins and L. Eisner. On Rutishauser’s approach to self-similar flows. SIAM journal on Matrix Analysis and Applications, 11 (1990), pp. 301–311.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, P.O. Box 398, Notre Dame, IN, 46556, USA

    L. Faybusovich

Authors
  1. L. Faybusovich
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Editor information

Editors and Affiliations

  1. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 138 W. Main Street, Urbana, IL, 61801, USA

    Paul Van Dooren

  2. Department of Mathematics, Ohio State University, 100 Mathematics Building, 231 West 18th Avenue, Columbus, OH, 43210-1174, USA

    Bostwick Wyman

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© 1994 Springer-Verlag New York, Inc.

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Faybusovich, L. (1994). On the Rutishauser’s Approach to Eigenvalue Problems. In: Van Dooren, P., Wyman, B. (eds) Linear Algebra for Control Theory. The IMA Volumes in Mathematics and its Applications, vol 62. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8419-9_8

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  • DOI: https://doi.org/10.1007/978-1-4613-8419-9_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8421-2

  • Online ISBN: 978-1-4613-8419-9

  • eBook Packages: Springer Book Archive

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