Locating real multiple zeros of a real interval polynomial

  • Authors:

  • Hiroshi Sekigawa;Kiyoshi Shirayanagi

  • Affiliations:

  • Nippon Telegraph and Telephone Corporation, Kanagawa, Japan;Nippon Telegraph and Telephone Corporation, Kanagawa, Japan

  • Venue:
  • Proceedings of the 2006 international symposium on Symbolic and algebraic computation
  • Year:
  • 2006

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Abstract

For a real interval polynomial F, we provide a rigorous method for deciding whether there exists a polynomial in F that has a multiple zero in a prescribed interval in R. We show that it is sufficient to examine a finite number of edge polynomials in F. An edge polynomial is a real interval polynomial such that the number of coefficients that are intervals is one. The decision method uses the property that a univariate polynomial is of degree one with respect to each coefficient regarded as a variable. Using this method, we can completely determine the set of real numbers each of which is a multiple zero of some polynomial in F.