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The Hadamard Factorization of Hurwitz and Schur stable Polynomials

  • J. Garloff
  • B. Srinivasan
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 121)

Abstract

We consider the Hadamard (i.e. the coefficient-wise) product of two poly nomials. The set of the Hurwitz stable polynomials is closed under the Hadamard product, whereas the set of the Schur stable polynomials is not. In this note we show that each Schur stable polynomial allows a Hadamard factorization into two Schur stable polynomials, whereas there are Hurwitz stable polynomials of degree 4 which do not have a Hadamard factorization into two Hurwitz stable polynomials of degree 4.

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References

  1. [1]
    GarlofF, J. and Wagner, D.G., Hadamard products of stable polynomials are stable, Technical Report no. 9402, FH Konstanz, Fachbereich Informatik, to appear in Journal Math. Analysis and Applications.Google Scholar
  2. [2]
    GarlofF, J. and Wagner, D.G., Preservation of total nonnegativity under the Hadamard product and related topics, Technical Report no. 9501, FH Konstanz, Fachbereich Informatik, pp. 6 11, to appear in Total Positivity and its Applications, M. Gasca and C.A. Micchelli, Eds., Kluwer Acad. Publ., 1995.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1996

Authors and Affiliations

  • J. Garloff
    • 1
  • B. Srinivasan
    • 2
  1. 1.Fachbereich InformatikFachhochschule KonstanzKonstanzGermany
  2. 2.Institut d’Automatique, DGMEPFL LausanneUSA

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