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Bezoutians Applied to Least Squares Approximation of Rational Functions

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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

A projection method to reduce large scale discrete systems which has been introduced in au][12, 21] will be generalized to continues systems without to transform it bilinear. To achieve that goal depending on an algebraic curve γ { ℂ and a rational function h ∈ ℂ(z) a non negative function F: ℂm » ℝ is introduced whose minimizer provides an approximant of degree m. Special cases are obtained via specification of γ and h.

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Author information

Authors and Affiliations

  1. Thiemstrasse 21, D-04299, Leipzig, Germany

    Sven Feldmann

Authors
  1. Sven Feldmann
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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

Additional information

To Georg Heinig

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Feldmann, S. (2010). Bezoutians Applied to Least Squares Approximation of Rational Functions. 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_12

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