skip to main content
10.1145/1141277.1141666acmconferencesArticle/Chapter ViewAbstractPublication PagessacConference Proceedingsconference-collections
Article

Pseudozero set of interval polynomials

Authors Info & Claims
Published:23 April 2006Publication History

ABSTRACT

Interval polynomials are useful to describe perturbed polynomials. We present a graphical tool to describe how perturbations of the polynomial coefficients affect its zeros without using interval arithmetic nor matrix representation. This tool implements real pseudozero set that differ from the well known complex pseudozero set restricting perturbations to be real and applied to real polynomials. We introduce a computable formula for this real pseudozero set and compare complex and real pseudozero sets. We propose a graphical MATLAB interface to draw zeros of such interval polynomials.

References

  1. The FRISCO Project, 2000. http://www.nag.co.uk/projects/FRISCO.html.Google ScholarGoogle Scholar
  2. W. Gautschi. On the condition of algebraic equations. Numer. Math., 21:405--424, 1973.Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. S. Graillat and P. Langlois. Testing polynomial primality with pseudozeros. In Proceedings of the Fifth Conference on Real Numbers and Computers, pages 231--246, Lyon, France, September 2003.Google ScholarGoogle Scholar
  4. S. Graillat and P. Langlois. Pseudozero set decides on polynomial stability. In Proceedings of the Symposium on Mathematical Theory of Networks and Systems, Leuven, Belgium, July 2004.Google ScholarGoogle Scholar
  5. D. Hinrichsen and B. Kelb. Spectral value sets: a graphical tool for robustness analysis. Systems Control Lett., 21(2):127--136, 1993. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. WWW resources about Interval Arithmetic. URL = http://www.cs.utep.edu/interval-comp/main.html.Google ScholarGoogle Scholar
  7. L. Jaulin, M. Kieffer, O. Didrit, and É. Walter. Applied interval analysis. Springer-Verlag London Ltd., London, 2001.Google ScholarGoogle ScholarCross RefCross Ref
  8. M. Karow. Geometry of spectral value sets. PhD thesis, Universitt Bremen, 2003.Google ScholarGoogle Scholar
  9. D. G. Luenberger. Optimization by vector space methods. John Wiley & Sons Inc., New York, 1969. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. M. Mignotte. Mathematics for computer algebra. Springer-Verlag, New York, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. R. G. Mosier. Root neighborhoods of a polynomial. Math. Comp., 47(175):265--273, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. A. M. Ostrowski. Solution of equations and systems of equations. Second edition. Pure and Applied Mathematics, Vol. 9. Academic Press, New York, 1966.Google ScholarGoogle Scholar
  13. H. J. Stetter. Polynomials with coefficients of limited accuracy. In Computer algebra in scientific computing---CASC'99 (Munich), pages 409--430. Springer, Berlin, 1999.Google ScholarGoogle Scholar
  14. H. J. Stetter. Numerical Polynomial Algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. J. H. Wilkinson. Rounding errors in algebraic processes. Dover Publications Inc., New York, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Pseudozero set of interval polynomials

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in
      • Published in

        cover image ACM Conferences
        SAC '06: Proceedings of the 2006 ACM symposium on Applied computing
        April 2006
        1967 pages
        ISBN:1595931082
        DOI:10.1145/1141277

        Copyright © 2006 ACM

        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 23 April 2006

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • Article

        Acceptance Rates

        Overall Acceptance Rate1,650of6,669submissions,25%
      • Article Metrics

        • Downloads (Last 12 months)1
        • Downloads (Last 6 weeks)1

        Other Metrics

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader