Skip to main content

Gradient newton flows for complex polynomials

  • Conference paper
  • First Online:
Optimization

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1405))

  • 780 Accesses

Abstract

For a class of functions, closely related to the complex polynomials, the so-called Gradient Newton flows are studied. Attention is paid to structural stability and global convergence aspects. In the special case of polynomials of degree 3, a complete description of the local and global features of the involved phase-portraits is given.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Branin, F.H., A widely convergent method for finding multiple solutions of simultaneous non-linear equations, IBM J. Res. Develop. (1972), 504–522.

    Google Scholar 

  2. Bröcker, Th., Differentiable Germs and Catastrophes, London Math. Society Lect. Notes 17, Cambridge Univ. Press 1975.

    Google Scholar 

  3. Diener, I., On the global convergence of path-following methods to determine all solutions to a system of non-linear equations, NAM Bericht 47, Göttingen (1985).

    Google Scholar 

  4. Gibson, C.G., Wirthmüller, K., Plessis, A.A. du, Looijenga, E.J.N., Topological Stability of Smooth Mappings, Lect. Notes Math. 552, Springer Verlag 1976.

    Google Scholar 

  5. Jongen, H.Th., Jonker, P., Twilt, F., Nonlinear optimization in IRn, part II: Transversality, Flows, Parametric Aspects, Methoden und Verfahren der Mathematischen Physik, 32, Peter Lang Verlag, Frankfurt a.M., Bern, New York 1986.

    Google Scholar 

  6. Jongen, H.Th., Jonker, P., Twilt, F., On the classification of plane graphs representing structurally stable rational Newton flows, Memorandum Nr. 750, University of Twente, Enschede, The Netherlands (1988); to appear in J. Comb. Theory, series B.

    Google Scholar 

  7. Jongen, H.Th., Jonker, P., Twilt, F., The continuous desingularized Newton method for meromorphic functions, Acta Applicandae Mathematica 13 (1988), 81–121.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Lang, S., Algebra, Addison Wesley Publ. 1965.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Szymon Dolecki

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer Verlag

About this paper

Cite this paper

Twilt, F., Jonker, P., Streng, M. (1989). Gradient newton flows for complex polynomials. In: Dolecki, S. (eds) Optimization. Lecture Notes in Mathematics, vol 1405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083595

Download citation

  • DOI: https://doi.org/10.1007/BFb0083595

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51970-6

  • Online ISBN: 978-3-540-46867-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics