Skip to main content

The continuous Newton-method for meromorphic functions

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 810)

Keywords

  • Entire Function
  • Meromorphic Function
  • Stable Manifold
  • Extended Tree
  • Transcendental Entire Function

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L.V. Alfohrs: Complex Analysis, Mac Graw Hill Book Company (1953).

    Google Scholar 

  2. A.A. Andronov, E.L. Leontovich, I.I. Gordon and A.G. Maier: Qualitative theory of second-order dynamical systems, John Wiley & Sons, inc. (1973)

    Google Scholar 

  3. A.A. Andronov, E.L. Leontovich, I.I. Gordon and A.G. Maier: Theory on bifurcations of dynamical systems on a plane, John Wiley & Sons, inc. (1973).

    Google Scholar 

  4. N. Bourbaki: Eléments de Mathématique, Topologie Générale, chap. 1, Hermann (1961).

    Google Scholar 

  5. D. Braess: Ueber die Einzugsbereiche der Nullstellen von Polynomen beim Newton Verfahren, Numer. Math. 29, pp. 123–132 (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. F.H. Branin, Jr.: A widely convergent method for finding multiple solutions of simultaneous nonlinear equations, I.B.M. — J.Res.Develop. (1972), pp. 504–522.

    Google Scholar 

  7. J. Gomulka: Remarks on Branin's method for solving nonlinear equations, In: Towards Global Optimization, Ed.: L.C.W. Dixon and G.P. Szegö, North-Holland Publishing Company (1975).

    Google Scholar 

  8. L.C.W. Dixon, J. Gomulka and S.E. Hersom: Reflections on the Global Problem, In: Optimization in Action, L.C.W. Dixon (ed.), Acad. Press (1976).

    Google Scholar 

  9. V. Guillemin, A. Pollack: Differential Topology, Prentice Hall, inc. (1974).

    Google Scholar 

  10. P. Hartman: Ordinary Differential Equations, John Wiley & Sons, inc. (1964).

    Google Scholar 

  11. M. Henle: A Combinatorial Introduction to Topology, W.H. Freeman & Company (1979).

    Google Scholar 

  12. M.W. Hirsch: Differential Topology, Springer Verlag (1976).

    Google Scholar 

  13. A.S.B. Holland: Introduction to the theory of entire functions, Acad. Press (1973).

    Google Scholar 

  14. H.Th. Jongen, P. Jonker, F. Twilt: On Newton Flows in Optimization. In: Proc. III Symp. OPERATIONS RESEARCH, Ed. Werner Oettli, Franz Steffens, Methods of Operations Research 31 (1979).

    Google Scholar 

  15. S. Lang, Algebra, Addison-Wesley Publish. Company.

    Google Scholar 

  16. S. Lefschetz: Differential equations, Geometric theory, Interscience Publ.

    Google Scholar 

  17. A.I. Markushevich: Theory of functions of a complex variable II, Prentice Hall, inc. (1965).

    Google Scholar 

  18. A.I. Markushevich: Theory of functions of a complex variable III, Prentice Hall, inc. (1965).

    Google Scholar 

  19. R. Nevanlinna: Eindeutige analytische Funktionen, Springer Verlag (1953).

    Google Scholar 

  20. M.M. Peixoto: Structural stability on two-dimensional manifolds, Topology 1, pp. 101–120 (1962).

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. M.M. Peixoto; On the Classification of Flows on 2-Manifolds, In: Dynamical Systems, Ed. M.M. Peixoto, Acad. Press (1973).

    Google Scholar 

  22. S. Smale: A convergent process of price adjustment and global Newton methods, J.Math.Economics 3 (1976), pp. 107–120.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. E.H. Spanier: Algebraic Topology, Mac Graw Hill Book Company (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Jongen, H., Jonker, P., Twilt, F. (1980). The continuous Newton-method for meromorphic functions. In: Martini, R. (eds) Geometrical Approaches to Differential Equations. Lecture Notes in Mathematics, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089981

Download citation

  • DOI: https://doi.org/10.1007/BFb0089981

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10018-8

  • Online ISBN: 978-3-540-38166-2

  • eBook Packages: Springer Book Archive