Skip to main content
SpringerLink
Log in

Enclosure of the Zero Set of Multivariate Exponential Interval Polynomials

  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

The zero set of one general multivariate exponential polynomial with interval coefficients is enclosed by unions and intersections of closed half-spaces. Tighter enclosures are derived in the bivariate case. Common zeros of polynomial systems can be located by an appropriate intersection of these enclosure sets in an appropriate space. The resulting domains are directly brought into polynomial equation solvers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F.G. Boese and W. Luther, Enclosure of the zero set of polynomials in several complex variables, Multidimens. Systems Signal Process. 12(2) (2001) 165–197.

    Google Scholar 

  2. F.G. Boese and W. Luther, Accurate enclosure of the zero set of multivariate polynomials, BIT 43(2) (2003) 245–261.

    Google Scholar 

  3. N.K. Bose, Applied Multidimensional Systems Theory (Van Nostrand Reinhold, New York, 1982).

    Google Scholar 

  4. A.M. Cohen, H. Cuypers and H. Sterk, eds., Some Tapas of Computer Algebra (Springer, Berlin, 1999).

    Google Scholar 

  5. D. Fausten and W. Luther, Verified solution of systems of nonlinear polynomial equations, in: Validated Numerics, Interval Methods, eds. W. Krämer and W.J. von Gudenberg (Kluwer Academic, Dordrecht, 2001) pp. 141–152.

    Google Scholar 

  6. G. Fruchter, U. Srebro and E. Zeheb, Conditions on the boundary of the zero set and application to stabilization of systems with uncertainty, J. Math. Anal. Appl. 161 (1991) 148–175.

    Google Scholar 

  7. R. Hammer, M. Hocks, U. Kulisch and D. Ratz, Numerical Toolbox for Verified Computing I (Springer, Berlin, 1993).

    Google Scholar 

  8. E. Hille, Analytic Function Theory, Vol. II (Chelsea, New York, 1962).

    Google Scholar 

  9. E.I. Jury, Stability of multidimensional systems and related problems, in: Multidimensional Systems, Techniques and Applications, ed. S.G. Tzafestas (Marcel Dekker, New York, 1986) pp. 89–159.

    Google Scholar 

  10. B. Sturmfels, Polynomial equations and convex polytopes, Amer. Math. Monthly 105 (1998) 907–922.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für extraterrestrische Physik, Garching, Germany

    Fritz G. Boese

  2. Institut für Informatik und Interaktive Systeme, University of Duisburg–Essen, Germany

    Wolfram J. Luther

Authors
  1. Fritz G. Boese
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wolfram J. Luther
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boese, F.G., Luther, W.J. Enclosure of the Zero Set of Multivariate Exponential Interval Polynomials. Numerical Algorithms 37, 35–44 (2004). https://doi.org/10.1023/B:NUMA.0000049486.95047.25

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:NUMA.0000049486.95047.25

Search

Navigation