Skip to main content
SpringerLink
Log in

Incomplete Newton-Ulm method for large scale nonlinear equations

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

This paper presents an incomplete Newton-Ulm method (INU) for nonlinear equations. This method uses parts of elements of Jacobian matrix to obtain the next iteration point and does not contain inverse operators in its expression. We discuss and analyze the convergence conditions and semilocal convergence of the new method. Some special INU algorithms are designed and numerical experiments are given. Numerical results show that INU method is effective for large scale nonlinear equations.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Moser, J.: Stable and random motions in dynamical systems with special emphasis on celestial mechanica. HermanWeil Lectures, Annals of Mathematics Studies, vol. 77. Princeton University Press, Princeton, NJ (1973)

    Google Scholar 

  2. Hald, O.H.: On a Newton-Moser type method. Number. Math. 23, 411–425 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ulm, S.: On iterative methods with successive approximation of the inverse operator(Russian). Izv. Akad. Nauk Est. SSR 16, 403–411 (1967)

    MathSciNet  Google Scholar 

  4. Zehnder, E.J.: A remark about Newton’s method. Commun. Pure Appl. Math. 27, 361–366 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  5. Petzeltova, H.: Remark on Newton-Moser type method. Commentat. Math. Univ. Carol. 21, 719–725 (1980)

    MathSciNet  MATH  Google Scholar 

  6. Gutiérrez, J.M., Hernández, M.A., Romero, N.: A note on a modification of Moser’s method. J. Complex. 24, 185–197 (2008)

    Article  MATH  Google Scholar 

  7. Wang, D.R., Zhao, F.G.: The theory of Smale’s point estimation and its applications. J. Comput. Appl. Math. 60, 253–269 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Argyros, I.K.: On Ulm’s method for Fréchet differentiable operators. J. Appl. Math. Comput. 31, 97–111 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Argyros, I.K.: On Ulm’s method forusing divided differences of order one. Numer. Algor. 52, 295–320 (2009)

    Article  MATH  Google Scholar 

  10. Ezquerro, J.A., Hernández, M.A.: An Ulm-type method with R-order of convergence three. Nonliner Anal.: Real World Appl. 13, 14–26 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu, H., Ni, Q.: Incomplete Jacobian Newton method for nonlinear equations. J. Comput. Appl. Math. 56, 218–227 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Sciences, China University of Mining and Technology, Xuzhou, 221008, People’s Republic of China

    H. J. Wang, F. Chen & Q. Wang

  2. College of Sciences, Nanjing University of Technology, Nanjing, 210009, People’s Republic of China

    H. Liu

Authors
  1. H. J. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Q. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to H. J. Wang or H. Liu.

Additional information

This work is supported by the Jiangsu Province Natural Science Foundation of China (BK20151139) and Fundamental Research Funds for the Central Universities(2012LWA10)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, H.J., Chen, F., Liu, H. et al. Incomplete Newton-Ulm method for large scale nonlinear equations. Numer Algor 72, 409–424 (2016). https://doi.org/10.1007/s11075-015-0052-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-015-0052-0

Keywords

Search

Navigation