Skip to main content
SpringerLink
Log in

Interval iterations for including a set of solutions

Intervalliterationen zur Einschließung einer Lösungsmenge

  • Contributed Papers
  • Published:
Computing Aims and scope Submit manuscript

Abstract

For including a set of solutions of a function strip we apply interval iterations. To construct a sequence of intervals converging to a fix-interval or a pseudofix-interval we make use of three kinds of interval operators with different properties and two iteration methods which are in accordance with the assumptions.

Zusammenfassung

Zur Einschließung einer Lösungsmenge eines Funktionsstreifens werden Intervall-Iterationsverfahren angewandt. Um eine Intervallfolge zu erzeugen, welche gegen ein Fixintervall oder Pseudo-Fixintervall konvergiert, werden drei Arten von Intervalloperatoren angegeben, sowie zwei Iterationsmethoden in Abhängigkeit von entsprechenden Voraussetzungen.

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. Gay, D. M.: Perturbation bounds for nonlinear equations. Siam J. Numer. Anal.18, 654–663 (1981).

    Article  Google Scholar 

  2. Krawczyk, R.: NEWTON-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Comp.4, 187–201 (1969).

    Article  Google Scholar 

  3. Krawczyk, R.: Intervalliterationsverfahren. Bericht Nr. 186 der Math.-Stat. Sektion, Graz (1982).

  4. Krawczyk, R.: Intervalloperatoren einer Funktion, deren Lipschitzmatrix eineM-Intervallmatrix ist. Freiburger Intervall-Bericht 82/10, 1–19 (1982).

    Google Scholar 

  5. Krawczyk, R., Selsmark, F.: Order-convergence and iterative interval methods. J. Math. Anal. and Appl.73, 1–23 (1980).

    Article  Google Scholar 

  6. Moore, R. E.: Interval analysis. Englewood Cliffs, N. J.: Prentice-Hall 1966.

    Google Scholar 

  7. Moore, R. E.: A test for existence of solutions to nonlinear systems. SIAM J. Num. Anal.14, 611–615 (1977).

    Article  Google Scholar 

  8. Nickel, K.: Die Überschätzung des Wertebereiches einer Funktion in der Intervallrechnung mit Anwendungen auf lineare Gleichungssysteme. Comp.18, 15–36 (1977).

    Google Scholar 

  9. Nuding, E.: Intervallarithmetik, Teil 2. Rechenzentrum, Universität Heidelberg, 1972.

  10. Qi, L.: A generalization of the Krawczyk-Moore Algorithm. In: Interval Mathematics (Nickel, K., ed.), pp. 481–488. New York-London: Academic Press 1980.

    Google Scholar 

  11. Rump, S. M.: Kleine Fehlerschranken bei Matrixproblemen. Dissertation, Wuppertal, 1980.

Download references

Author information

Authors and Affiliations

  1. Bohlweg 2, D-3392, Clausthal-Zellerfeld, Federal Republic of Germany

    R. Krawczyk

Authors
  1. R. Krawczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Professor Dr. K. Nickel on the occasion of his 60th birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krawczyk, R. Interval iterations for including a set of solutions. Computing 32, 13–31 (1984). https://doi.org/10.1007/BF02243016

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02243016

Keywords

Search

Navigation