Skip to main content

Solving Large nonlinear systems of equations arising in mechanics

Part of the Lecture Notes in Mathematics book series (LNM,volume 909)

Keywords

  • Conjugate Gradient
  • Line Search
  • Gradient Evaluation
  • BFGS Method
  • Inexact Newton Method

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. Axelsson, O.; On preconditioning and convergence acceleration in sparse matrix problems. Report 74-10, Data Handling Division, CERN, Geneva (1974).

    MATH  Google Scholar 

  2. Concus, P., Golub, G., O'Leary, D.; Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method, Computing 19, 321–339 (1978).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Curtis, A., Powell, M., Reid, J.; On the estimation of sparse Jacobian matrices, J. Inst. Math. Appl. Vol. 13, 117–119, (1974).

    CrossRef  MATH  Google Scholar 

  4. Dembo, R., Eisenstat, S., Steihaug, T.; Inexact Newton methods, Tech. Report Series B: No. 47, School of Organization and Management, Yale University (1980).

    Google Scholar 

  5. Hesteness, M., Stiefel, E.; Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stand. 49, 409–436 (1952).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Matthies, H., Stang, G.; The solution of nonlinear finite element equations, Inter. J. of Num. Meth. in Eng. Vol. 14, (1979).

    Google Scholar 

  7. Meijerink, J., van der Vorst, H.; An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comp. 31, 148–162 (1977).

    MathSciNet  MATH  Google Scholar 

  8. Nocedal, J.; Updating quasi-Newton matrices with limited storage, Math. Comp. Vol. 35, 773–782 (1980).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Ortega, J., Rheinboldt, W.; Iterative solution of nonlinear equations in several variables, Academic Press (1970).

    Google Scholar 

  10. Shanno, D., Phua, K.; A variable method subroutine for unconstrained nonlinear minimization, MIS. Tech. Rep. No. 28, University of Arizona (1978).

    Google Scholar 

  11. Young, D.; Iterative solution of large linear systems, Academic Press (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Nocedal, J. (1982). Solving Large nonlinear systems of equations arising in mechanics. In: Hennart, J.P. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092967

Download citation

  • DOI: https://doi.org/10.1007/BFb0092967

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11193-1

  • Online ISBN: 978-3-540-38986-6

  • eBook Packages: Springer Book Archive