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Introduction to Bezoutians

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Numerical Methods for Structured Matrices and Applications

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

Abstract

In the present paper we consider classes of matrices the entries of which are in a given field F. These matrices have a special structure, they are Bezoutians. Historically, Bezoutians were at first introduced in connection with the elimination for the solution of systems of nonlinear algebraic equations and in connection with root localization problems. Only much later their importance for Hankel and Toeplitz matrix inversion became clear.

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Authors and Affiliations

  1. Dept. of Mathematics, Chemnitz University of Technology, Reichenhainer Straße 39, D-09126, Chemnitz, Germany

    Karla Rost

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  1. Karla Rost
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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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Rost, K. (2010). Introduction to Bezoutians. 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_3

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