Skip to main content

Interval test and existence theorem

  • Conference paper
  • First Online:
  • 159 Accesses

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. Avila, J.H.: The feasibility of continuation methods for nonlinear equations, SIAM. J. Numer. Anal. 11 (1974).

    Google Scholar 

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

    Google Scholar 

  3. Krawczyk, R.: Zentrische Formen und Intervalloperatoren, Freiburger Intervall-Berichte 82/1, 1–30 (1982).

    Google Scholar 

  4. Krawczyk, R.: Intervallsteigungen für rationale Funktionen und zugeordnete zentrische Formen. Freiburger Intervall-Berichte 83/2, 1–30 (1983).

    Google Scholar 

  5. Hansen, E.R.: The centred form. in: Topics in Interval Analysis, (E.R. Hansen, Ed.) Oxford, pp. 102–105.

    Google Scholar 

  6. Mihai Cristea: A note on global inversion theorems and applications to differential equations. Nonlinear Analysis, Theory, Methods and Applic., pp. 1155–1161 (1981).

    Google Scholar 

  7. Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs, NJ (1966).

    Google Scholar 

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

    Article  Google Scholar 

  9. Moore, R.E.: Methods and Applications of Interval Analysis. SIAM Publications, Philadelphia (1974).

    Google Scholar 

  10. Moore, R.E., and Qi, L.: A successive interval test for nonlinear systems, SIAM J. Numer. Anal. 19 (1982).

    Google Scholar 

  11. Moore, R.E., and Zuhe Shen: An interval version of Chebyshev's method for nonlinear operator equations. Nonlinear Analysis, Theory, Methods and Applic. 7, 21–34 (1983).

    Google Scholar 

  12. Neumaier, A.: Interval norms, Freiburger Intervall-Berichte 81/5, 17–33 (1981).

    Google Scholar 

  13. Nickel, K.: On the Newton method in interval analysis. MRC Report No. 1136, Mathematics Research Center. University of Wisconsin-Madison, (1971).

    Google Scholar 

  14. Ortega, J.M., and Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York-London (1970).

    Google Scholar 

  15. Plastock. R.: Homeomorphism between Banach spaces. Trans. Amer. Math. Soc., 200, 169–183 (1974).

    Google Scholar 

  16. Pourciau, B.H.: Analysis and optimization of Lipschitz continuous mappings. J. Optim. Theory Appl. 22, 311–351 (1977).

    Article  Google Scholar 

  17. Radulescu, M., and Radulescu, S.: Global inversion theorem and applications to differential equations. Nonlinear Analysis, Theory, Methods and Applic. 4, 951–965 (1980).

    Google Scholar 

  18. Ratschek, H.: Zentrische Formen. ZAMM 58, 434–436 (1978).

    Google Scholar 

  19. Schwetlick, H.: Numerische Lösung nichtlinearer Gleichungen, VEB Deutscher Verlag des Wissenschaften, Berlin, 1978.

    Google Scholar 

  20. Zuhe, Shen: On some classical existence theorems. Nonlinear Analysis, Theory, Methods and Applic. 7, 1024–1033 (1983).

    Google Scholar 

  21. Zuhe, Shen: Diffeomorphism and the feasibility of the numerical continuation methods. Nonlinear Analysis, Theory, Methods and Applics. 9, 495–502 (1985).

    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

Shen, Z. (1986). Interval test and existence theorem. 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_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-16437-5_17

  • 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