BIT Numerical Mathematics

, Volume 28, Issue 1, pp 80–87 | Cite as

Optimal centered forms

  • Eckart Baumann
Part II Numerical Mathematics

Abstract

A simple expression for an “optimal” center of a centered form is presented. Among all possible centers within a given interval this center yields the greatest lower bound or the lowest upper bound of a centered form, respectively. It is also shown that one-sided isotonicity holds for such centered forms.

AMS Subject Classifications

65G10 

Keywords

interval arithmetic optimal centered form one-sided isotonicity global optimization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Baumann,Globale Optimierung stetig differenzierbarer Funktionen einer Variablen, Freiburger Intervall-Berichte 86/6 (1986).Google Scholar
  2. 2.
    O. Caprani and K. Madsen,Mean value forms in interval analysis, Computing 25, 147–154 (1980).Google Scholar
  3. 3.
    W. Chuba and W. Miller,Quadratic convergence in interval arithmetic, Part I. BIT 12, 184–290 (1972).Google Scholar
  4. 4.
    E. R. Hansen,The centered form, pp. 102–106, in Topics in Interval Analysis (E. R. Hansen, ed.), Oxford, Clarendon Press (1969).Google Scholar
  5. 5.
    R. Krawczyk and K. Nickel,Die zentrische Form in der Intervallarithmetik, ihre quadratische Konvergenz und ihre Inklusionsisotonie, Computing 28, 117–137 (1982).Google Scholar
  6. 6.
    R. Krawczyk and A. Neumaier,Interval slopes for rational functions and associated centered forms, SIAM J. Numer. Anal., Vol. 22, No. 3 (1985).Google Scholar
  7. 7.
    H. Ratschek and J. Rokne,Computer Methods for the Range of Functions, Ellis Horwood Ltd. (1984).Google Scholar

Copyright information

© BIT Foundations 1988

Authors and Affiliations

  • Eckart Baumann
    • 1
  1. 1.Institut für Angewandte Mathematik der Universität FreiburgFreiburg i. Br.West Germany

Personalised recommendations