Skip to main content

Convergent bounds for the range of multivariate polynomials

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 212))

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alefeld, G. and J. Herzberger, Introduction to Interval Computations, Academic Press, New York (1983)

    Google Scholar 

  2. Bickard, T.A. and E.I. Jury, Real polynomials: a test for non-global non-negativity and non-global positivity, J. Math. Anal. Appl. 78, 17–32 (1980).

    Article  Google Scholar 

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

    Google Scholar 

  4. Bose, N.K. and J.P. Guiver, Multivariate polynomial positivity invariance under coefficient perturbation, IEEE Trans. Acoust. Speech Signal Process ASSP — 28, 660–665 (1980).

    Google Scholar 

  5. Cargo, G.T. and O Shisha, The Bernstein form of a polynomial, J. Res. Nat. Bur. Standards 70B, 79–81 (1966).

    Google Scholar 

  6. Grassmann, E. and J. Rokne, The range of values of a circular complex polynomial over a circular complex interval, Computing 23, 139–169 (1979).

    Google Scholar 

  7. Hardy, G.H., J.E. Littlewood, and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, London and New York (1959).

    Google Scholar 

  8. Lane, J.M. and R.F. Riesenfeld, Bounds on a polynomial, BIT 21, 112–117 (1981).

    Google Scholar 

  9. Lorentz, G.G., Bernstein Polynomials, Univ. Toronto Press, Toronto (1953)

    Google Scholar 

  10. Ratschek, H. and J. Rokne, Computer Methods for the Range of Functions, Ellis Horwood Ltd., Chichester (1984).

    Google Scholar 

  11. Rheinboldt, W.C., C.K. Mesztenyi, and J.M. Fitzgerald, On the evaluation of multivariate polynomials and their derivatives, BIT 17, 437–450 (1977).

    Google Scholar 

  12. Rivlin, T.J., Bounds on a polynomial, J. Res. Nat. Bur. Standards 74B, 47–54 (1970).

    Google Scholar 

  13. Rokne, J., Bounds for an interval polynomial, Computing 18, 225–240 (1977).

    Google Scholar 

  14. Rokne, J., A note on the Bernstein algorithm for bounds for interval polynomials, Computing 21, 159–170 (1979).

    Google Scholar 

  15. Rokne, J., The range of values of a complex polynomial over a complex interval, Computing 22, 153–169 (1979).

    Google Scholar 

  16. Rokne, J., Optimal computation of the Bernstein algorithm for the bound of an interval polynomial, Computing 28, 239–246 (1982).

    Google Scholar 

  17. Walach, E. and E. Zeheb, Sign test of multivariable real polynomials, IEEE Trans. Circuits and Systems CAS-27, 619–625 (1980).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Karl Nickel

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Garloff, J. (1986). Convergent bounds for the range of multivariate polynomials. In: Nickel, K. (eds) Interval Mathematics 1985. IMath 1985. Lecture Notes in Computer Science, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16437-5_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-16437-5_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16437-1

  • Online ISBN: 978-3-540-39779-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics