Skip to main content

Continuation methods and parametrized nonlinear least squares: Techniques and experiments

  • Conference paper
  • First Online:
Numerical Methods

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1005))

  • 617 Accesses

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. Allgower, E., and Georg, K., "Simplicial and continuation methods for approximating fixed points and solutions to systems of equations," SIAM Review 22 no. 1, pp. 28–85, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  2. Dennis, J.E., "An update for parametrized nonlinear least squares," private communication, 1982.

    Google Scholar 

  3. Dennis, J.E., and Schnabel, R.B., Numerical Methods for Unconstrained Optimization and Nonlinear Least Squares, to appear, 1982.

    Google Scholar 

  4. Dennis, J.E., Gay, D.M., and Welsch, R.E., "An adaptive nonlinear leastsquares algorithm," Technical Summary Report no. 2010, Mathematics Research Center, University of Wisconsin, 1979.

    Google Scholar 

  5. Garcia, C.B., and Zangwill, W.I., Pathways to Solutions, Fixed Points, and Equilibria, Prentice-Hall, 1981.

    Google Scholar 

  6. Georg, K., "On tracing an implicitly defined curve by quasi-Newton steps and calculating bifurcation by local perturbations," SIAM Journal on Scientific and Statistical Computing 2 no. 1, pp. 35–50, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  7. Kearfott, R.B., "A derivative-free arc continuation method and a bifurcation technique," Springer Lecture Notes no. 878, 1981.

    Google Scholar 

  8. Kearfott, R.B., "Some general bifurcation techniques," to appear in the SIAM Journal on Scientific and Statistical Computing.

    Google Scholar 

  9. Li, T.Y., and Yorke, J.A., "A simple reliable numerical algorithm for following homotopy paths," in Analysis and Computation of Fixed Points, ed. S.M. Robinson, Academic Press, 1979.

    Google Scholar 

  10. More', J.J., Garbow, B.S., and Hillstrom, K.E., "Testing unconstrained optimization software," ACM Transactions on Mathematical Software 7 no. 1, pp. 17–41, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  11. Ortega, J.M., and Rheinboldt, W.C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, 1970.

    Google Scholar 

  12. de Villiers, N., and Glasser, D., "A continuation method for nonlinear regression," SIAM Journal on Numerical Analysis 18 no. 6, pp. 1139–1154, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  13. Watson, L.T., "Engineering applications of the Chow-Yorke Algorithm," Applied Mathematics and Computing, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Kearfott, R.B. (1983). Continuation methods and parametrized nonlinear least squares: Techniques and experiments. In: Numerical Methods. Lecture Notes in Mathematics, vol 1005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0112531

Download citation

  • DOI: https://doi.org/10.1007/BFb0112531

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12334-7

  • Online ISBN: 978-3-540-40967-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics