[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content

On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

We present a modified method for solving nonlinear systems of equations with order of convergence higher than other competitive methods. We generalize also the efficiency index used in the one-dimensional case to several variables. Finally, we show some numerical examples, where the theoretical results obtained in this paper are applied.

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

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ostrowski, A.M.: Solutions of Equations in Euclidean and Banach Spaces. Academic Press, New York (1973)

    Google Scholar 

  2. Argyros, I.K., Chen, D., Qian, Q.: A local convergence theorem for the super-Halley method in a Banach space. Appl. Math. Lett. 7(5), 49–52 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs (1964)

    MATH  Google Scholar 

  4. Grau, M., Díaz-Barrero, J.L.: An improvement of the Euler–Chebyshev iterative method. J. Math. Anal. Appl. 315, 1–7 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Schröder, E.: Über unendlich viele Algorithmen zur Auflösung der Gleichungen. Math. Ann. 2, 317–365 (1870)

    Article  MathSciNet  Google Scholar 

  6. Grau-Sánchez, M., Grau, A., Noguera, M.: Frozen divided difference scheme for solving systems of nonlinear equations. J. Comput. Appl. Math. 235, 1739–1743 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Potra, F.A., Pták, V.: A generalization of Regula Falsi. Numer. Math. 36, 333–346 (1981)

    Article  MATH  Google Scholar 

  8. Potra, F.A., Pták, V.: Nondiscrete Induction and Iterative Processes. Research Notes in Mathematics, vol. 103. Wiley, Boston–London–Melbourne (1984)

    MATH  Google Scholar 

  9. Polyanin, A.D., Manzhirov, A.V.: Handbook of Integral Equations. CRC Press, Boca Ratón (1998)

    Book  MATH  Google Scholar 

  10. Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13, 87–93 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chandrasekhar, D.: Radiative Transfer. Dover, New York (1960)

    Google Scholar 

  12. Argyros, I.K.: Quadratic equations and applications to Chandrasekhar’s and related equations. Bull. Aust. Math. Soc. 32(2), 275–292 (1985)

    Article  MATH  Google Scholar 

  13. Argyros, I.K.: On a class of nonlinear integral equations arising in neutron transport. Aequ. Math. 35, 99–111 (1988)

    Article  Google Scholar 

  14. Ezquerro, J.A., Gutiérrez, J.M., Hernández, M.A., Salanova, M.A.: Solving nonlinear integral equations arising in radiative transfer. Numer. Funct. Anal. Optim. 20, 661–673 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Fousse, L., Hanrot, G., Lefèvre, V., Pélissier, P., Zimmermann, P.: MPFR: a multiple-precision binary floating-point library with correct rounding. ACM Trans. Math. Softw. 33(2), 15 (2007)

    Article  Google Scholar 

  16. http://www.mpfr.org/mpfr-2.1.0/timings.html

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. A. Ezquerro.

Additional information

Communicated by Florian A. Potra.

This work was supported in part by the Spanish Ministry of Science and Innovation (MTM 2008-01952/MTM) and the Riojan Autonomous Community (Project Colabora 2009/04).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ezquerro, J.A., Grau-Sánchez, M., Grau, A. et al. On Iterative Methods with Accelerated Convergence for Solving Systems of Nonlinear Equations. J Optim Theory Appl 151, 163–174 (2011). https://doi.org/10.1007/s10957-011-9870-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-011-9870-y

Keywords