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On Extremal Problems of Interpolation Theory with Unique Solution

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Numerical Methods for Structured Matrices and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 199))

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Abstract

The main goal of this paper is to investigate the matrix extremal interpolation problem formulated in Chapter 7 of the monograph [7]. We give natural conditions under which the problem has one and only one solution. The basic idea of the proof is to use the matrix Riccati equation deduced in [7, Chapter 7].

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References

  1. Akhiezer, N.I.: On a minimum problem in function theory and the number of roots of an algebraic equation inside the unit disc (Russian), Izv. Akad. Nauk SSR, Otdel. Mat. i Est. Nauk 9 (1930), 1169–1189, English Translation in: Topics in Interpolation Theory (Eds.: H. Dym, B. Fritzsche, V.E. Katsnelson, B. Kirstein), OT Series, Volume 95, Birkhäuser, Basel-Boston-Berlin 1997, pp. 19–35.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Leipzig, Postfach: 10 09 20, D-04009, Leipzig, Germany

    Bernd Fritzsche & Bernd Kirstein

  2. 99 Cove Avenue, Milford, CT, 06461, USA

    Lev A. Sakhnovich

Authors
  1. Bernd Fritzsche
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  2. Bernd Kirstein
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  3. Lev A. Sakhnovich
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, 56127, Pisa, Italy

    Dario Andrea Bini

  2. Institut für Mathematik, Technische Universität Berlin, Straβe des 17. Juni 136, 10623, Berlin, Germany

    Volker Mehrmann

  3. Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-9, Storrs, CT, 06269, USA

    Vadim Olshevsky

  4. Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina Street, 8, Moscow, 119991, Russia

    Eugene E. Tyrtyshnikov

  5. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001, Leuven (Heverlee), Belgium

    Marc van Barel

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Dedicated to the memory of Georg Heinig

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© 2010 Birkhäuser Verlag Basel/Switzerland

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Fritzsche, B., Kirstein, B., Sakhnovich, L.A. (2010). On Extremal Problems of Interpolation Theory with Unique Solution. In: Bini, D.A., Mehrmann, V., Olshevsky, V., Tyrtyshnikov, E.E., van Barel, M. (eds) Numerical Methods for Structured Matrices and Applications. Operator Theory: Advances and Applications, vol 199. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8996-3_14

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