BIT Numerical Mathematics

, Volume 21, Issue 1, pp 112–117 | Cite as

Bounds on a polynomial

  • Jeffrey M. Lane
  • R. F. Riesenfeld
Part II Numerical Mathematics

Abstract

Methods are given for isolating and approximating the maxima, minima, and real roots of a polynomial with real coefficients. The methods are based on a variation diminishing property of the Bernstein coefficients of the polynomial and use of a recursive bisection technique.

Keywords

Computational Mathematic Real Root Real Coefficient Bernstein Coefficient Bisection Technique 

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References

  1. 1.
    G. T. Cargo and O. Shisha,The Bernstein form of a polynomial, Journal of Research of the National Bureau of Standards, Vol. 70B, No. 1. (1966), 79–81.Google Scholar
  2. 2.
    T. J. Rivlin,Bounds on a polynomial, Journal of Research of the National Bureau of Standards, Vol. 74B, No. 1 (1970), 47–54.Google Scholar
  3. 3.
    J. Rokne,Bounds for an interval polyomial, Computing 18, 225–240 (1977).Google Scholar
  4. 4.
    A. R. Forrest,Interactive Interpolation and Approximation by Bezier Polynomials, Comp. J. Vol. 15, No. 1 (1972), 71–79.Google Scholar
  5. 5.
    J. M. Lane and R. F. Riesenfeld,A theoretical development for the computer generation and display of polynomial curves and surfaces, IEEE TPAMI, January, 1980.Google Scholar
  6. 6.
    George E. Collins and Ellis Horowitz,The minimum root separation of a polynomial, Mathematics of Computation, Vol. 28, No. 126, (1974), 589–597.Google Scholar
  7. 7.
    B. Datt and N. K. Govil,On the location of the zeros of a polynomial, Journal of Approximation Theory 24, 78–82 (1978).Google Scholar
  8. 8.
    M. A. Jekins and J. F. Traub,Principles for testing polynomial zerofinding programs, Carnegie-Mellon University Tech. Report, March 1974.Google Scholar
  9. 9.
    George E. Collins and Rüdiger Loos,Polynomial real root isolation by differentiation, Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation, 15–25.Google Scholar
  10. 10.
    George E. Collins and Alkiviadis G. Akritas,Polynomial real root isolation using Descartes rule of signs. Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation, 272–275.Google Scholar

Copyright information

© BIT Foundations 1981

Authors and Affiliations

  • Jeffrey M. Lane
    • 1
    • 2
  • R. F. Riesenfeld
    • 1
    • 2
  1. 1.Boeing Commercial Airplane CompanySeattleUSA
  2. 2.University of UtahSalt Lake CityUSA

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