Skip to main content

A relaxation stratery for the modified Newton method

Part of the Lecture Notes in Mathematics book series (LNM,volume 477)

Keywords

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amann, H.: Über die näherungsweise Lösung nichtlinearer Integralgleichungen. Numer. Math. 19, 29–45 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brown, K. M., Dennis jr., J. E.: Derivative-free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximation. Numer. Math. 18, 289–297 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  3. Broyden, C. G.: The convergence of single-rank quasi-Newton method. Math. Comp. 24, 365–382 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  4. Broyden, C. G.: The convergence of a class of double-rank minimization algorithms. J. Inst. Math. Applic., 6, 76–90 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bulirsch, R.: Die Mehrzielmethode zur numerischen Lösung von nichtlinearen Randwertproblemen und Aufgaben der optimalen Steuerung. Lecture “Flugbahnoptimierung” of the Carl-Cranz-Gesellschaft e. V., Oct. 1971

    Google Scholar 

  6. Bulirsch, R., Stoer, J., Deuflhard, P.: Numerical solution of nonlinear two-point boundary value problems I to be published in Numer. Math., Hanbook Series Approximation

    Google Scholar 

  7. Deuflhard, P.: A Modified Newton Method for the Solution of Ill-conditioned Systems of Nonlinear Equations with Application to Multiple Shooting. Numer. Math. 22, 289–315 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Goldstein, A. A.: Cauchy's Methode der Minimierung. Numer. Math. 4, 146–150 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  9. Householder, A. S.: Principles of Numerical Analysis. New York: Mc Graw-Hill, 1953

    MATH  Google Scholar 

  10. Kantorovič, L., Akilow, G.: Functional Analysis in Normed Spaces. Moscow: Fizmatgiz, 1959

    Google Scholar 

  11. Keller, H. B.: Numerical methods for two-point boundary value problems. London: Blaisdell, 1968

    MATH  Google Scholar 

  12. Meyer, G. H.: On solving nonlinear equations with a one-parameter operator imbedding. University of Maryland, Comp. Sc. C.: Techn. Rep. 67-50

    Google Scholar 

  13. Osborne, M. R.: On shooting methods for boundary value problems. J. Math. Anal. Appl. 27, 417–433 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  14. Penrose, R.: A ßeneralized Inverse for Matrices. Proc. Cambridge Philos. Soc. 51, 406–413 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rentrop, P.: Numerical Solution of the Singular Ginzburg-Landau Equation. to be published in Computing

    Google Scholar 

  16. Stoer, J.: Einführung in die Mumerische Mathemathik I. Heidelberger Taschenbuch105, Berlin-Heidelberg-New York: Springer, 1972

    Google Scholar 

  17. Stoer, J., Bulirsch, R.: Einführung in die Numerische Mathematik II. Heidelberger Taschenbuch 114, Berlin-Heidelberg-New York: Springer, 1973

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Deuflhard, P. (1975). A relaxation stratery for the modified Newton method. In: Bulirsch, R., Oettli, W., Stoer, J. (eds) Optimization and Optimal Control. Lecture Notes in Mathematics, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079167

Download citation

  • DOI: https://doi.org/10.1007/BFb0079167

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07393-2

  • Online ISBN: 978-3-540-37591-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics