Advertisement

How Fast can Moore’s Interval Integration Method Really be?

  • Jürgen Herzberger

Abstract

Moore’s interval integration method which uses only function evaluations of the integrant is interpreted as an approximation of the fundamental integration by Riemann-sums. In this way we can estimate the speed of convergence of this method and it is shown that its convergence factor of its linear convergence rate is bounded to below. This lower bound is shown to be sharp in the sense that there is a wide dass of functions for which it cannot be improved. In particular this is true for all rational functions only considered by Moore.

Keywords

Rational Expression Interval Arithmetic Outer Approximation Integration Error Interval Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alefeld, G., Herzberger, J. (1974) Einführung in die Intervallrechnung. BIWissenschaftsverlag, Wiesbaden 1974; English edition: Introduction to Interval Computations, Academic Press, New York 1983Google Scholar
  2. 2.
    Apostolatos, N., Kuliseh, U. (1967) Grundlagen einer Maschinenintervallarithmetik. Computing 2 (1967), 89–104MATHGoogle Scholar
  3. 3.
    Courant, R., John, F. (1989) Introduction to Calculus and Analysis I. SpringerVerlag, BerlinGoogle Scholar
  4. 4.
    Drager, L.D. (1987) A simple Theorem on Riemann integration, based on classroom experience. In: Mathematical Modelling- Classroom Notes in Applied Mathematics, M.S. Klamkin (ed.), SIAM, Philadelphia, pp. 188–192Google Scholar
  5. 5.
    Moore, R.E. (1966) Interval Analysis. Prentice-Hall Inc., Englewood-Cliffs N.J.MATHGoogle Scholar
  6. 6.
    Neumaier, A. (1990) Interval Methods for Systems of Equations. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Jürgen Herzberger
    • 1
  1. 1.Department of MathematicsUniversity of OldenburgOldenburgGermany

Personalised recommendations