Skip to main content

A fast solver for nonlinear eigenvalue problems

Multigrid Methods For Nonlinear Problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 953)


A numerical method recently proposed by the author is shown to be a very efficient and robust method for the solution of a class of discrete nonlinear eigenvalue problems. In particular it is applied to follow the relevant and the spurious solution curves. Numerical results show that also in the neighbourhood of turning or bifurcation points the work required is considerably less than for usual continuation procedures and that a larger steplength may be chosen. A corresponding multi-grid method is used for following spurious solution branches.


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, log in via an institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Beyn, W.-J. and Lorenz, J., Spurious solutions for discrete superlinear boundary value problems. Computing 28, 43–51 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bohl, E. Finite Modelle gewöhnlicher Randwertaufgaben. B. G. Teubner Verlag, Stuttgart 1981

    Book  MATH  Google Scholar 

  3. Georg, K., On the convergence of an inverse iteration method for nonlinear elliptic eigenvalue problems. Numer. Math. 32, 69–74 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mittelmann, H. D., An efficient algorithm for bifurcation problems of variational inequalities. Manuscript NA-81-14, Computer Science Dept., Stanford University 1981 (submitted for publication)

    Google Scholar 

  5. Mittelmann, H. D. Multi-grid methods for simple bifurcation problems. To appear in: W. Hackbusch, U. Trottenberg (eds.), Proceedings of the conference on multi-grid methods, Cologne 1981, Springer-Verlag

    Google Scholar 

  6. Paige, C. C. and Saunders, M. A., Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12, 617–629 (1975)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Rainer Ansorge Theodor Meis Willi Törnig

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Mittelmann, H.D. (1982). A fast solver for nonlinear eigenvalue problems. In: Ansorge, R., Meis, T., Törnig, W. (eds) Iterative Solution of Nonlinear Systems of Equations. Lecture Notes in Mathematics, vol 953. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11602-8

  • Online ISBN: 978-3-540-39379-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics